diff --git a/doc/src/sgml/spgist.sgml b/doc/src/sgml/spgist.sgml
index ea88ae45e5..9ed1f564ee 100644
--- a/doc/src/sgml/spgist.sgml
+++ b/doc/src/sgml/spgist.sgml
@@ -205,10 +205,12 @@
  </para>
 
  <para>
-  Leaf tuples of an <acronym>SP-GiST</acronym> tree contain values of the
-  same data type as the indexed column.  Leaf tuples at the root level will
-  always contain the original indexed data value, but leaf tuples at lower
-  levels might contain only a compressed representation, such as a suffix.
+  Leaf tuples of an <acronym>SP-GiST</acronym> tree usually contain values
+  of the same data type as the indexed column, although it is also possible
+  for them to contain lossy representations of the indexed column.
+  Leaf tuples stored at the root level will directly represent
+  the original indexed data value, but leaf tuples at lower
+  levels might contain only a partial value, such as a suffix.
   In that case the operator class support functions must be able to
   reconstruct the original value using information accumulated from the
   inner tuples that are passed through to reach the leaf level.
@@ -330,19 +332,26 @@ typedef struct spgConfigOut
      </para>
 
      <para>
-      <structfield>leafType</structfield> is typically the same as
-      <structfield>attType</structfield>.  For the reasons of backward
-      compatibility, method <function>config</function> can
-      leave <structfield>leafType</structfield> uninitialized; that would
-      give the same effect as setting <structfield>leafType</structfield> equal
-      to <structfield>attType</structfield>.  When <structfield>attType</structfield>
-      and <structfield>leafType</structfield> are different, then optional
+      <structfield>leafType</structfield> must match the index storage type
+      defined by the operator class's <structfield>opckeytype</structfield>
+      catalog entry.  For reasons of backward compatibility,
+      method <function>config</function> can
+      leave <structfield>leafType</structfield> uninitialized (zero);
+      that is interpreted as meaning <structfield>opckeytype</structfield>.
+      (Recall that <structfield>opckeytype</structfield> can in turn be zero,
+      implying the storage type is the same as the operator class's input
+      type, which is the most common situation.)  In what
+      follows, <structfield>leafType</structfield> should be understood as
+      referring to the fully resolved leaf data type.
+     </para>
+
+     <para>
+      When <structfield>attType</structfield>
+      and <structfield>leafType</structfield> are different, the optional
       method <function>compress</function> must be provided.
       Method <function>compress</function> is responsible
       for transformation of datums to be indexed from <structfield>attType</structfield>
       to <structfield>leafType</structfield>.
-      Note: both consistent functions will get <structfield>scankeys</structfield>
-      unchanged, without transformation using <function>compress</function>.
      </para>
      </listitem>
     </varlistentry>
@@ -677,8 +686,7 @@ typedef struct spgInnerConsistentOut
        <structfield>reconstructedValue</structfield> is the value reconstructed for the
        parent tuple; it is <literal>(Datum) 0</literal> at the root level or if the
        <function>inner_consistent</function> function did not provide a value at the
-       parent level. <structfield>reconstructedValue</structfield> is always of
-       <structname>spgConfigOut</structname>.<structfield>leafType</structfield> type.
+       parent level.
        <structfield>traversalValue</structfield> is a pointer to any traverse data
        passed down from the previous call of <function>inner_consistent</function>
        on the parent index tuple, or NULL at the root level.
@@ -713,9 +721,14 @@ typedef struct spgInnerConsistentOut
        necessarily so, so an array is used.)
        If value reconstruction is needed, set
        <structfield>reconstructedValues</structfield> to an array of the values
-       of <structname>spgConfigOut</structname>.<structfield>leafType</structfield> type
        reconstructed for each child node to be visited; otherwise, leave
        <structfield>reconstructedValues</structfield> as NULL.
+       The reconstructed values are assumed to be of type
+       <structname>spgConfigOut</structname>.<structfield>leafType</structfield>.
+       (However, since the core system will do nothing with them except
+       possibly copy them, it is sufficient for them to have the
+       same <literal>typlen</literal> and <literal>typbyval</literal>
+       properties as <structfield>leafType</structfield>.)
        If ordered search is performed, set <structfield>distances</structfield>
        to an array of distance values according to <structfield>orderbys</structfield>
        array (nodes with lowest distances will be processed first).  Leave it
@@ -797,8 +810,7 @@ typedef struct spgLeafConsistentOut
        <structfield>reconstructedValue</structfield> is the value reconstructed for the
        parent tuple; it is <literal>(Datum) 0</literal> at the root level or if the
        <function>inner_consistent</function> function did not provide a value at the
-       parent level. <structfield>reconstructedValue</structfield> is always of
-       <structname>spgConfigOut</structname>.<structfield>leafType</structfield> type.
+       parent level.
        <structfield>traversalValue</structfield> is a pointer to any traverse data
        passed down from the previous call of <function>inner_consistent</function>
        on the parent index tuple, or NULL at the root level.
@@ -816,8 +828,8 @@ typedef struct spgLeafConsistentOut
        The function must return <literal>true</literal> if the leaf tuple matches the
        query, or <literal>false</literal> if not.  In the <literal>true</literal> case,
        if <structfield>returnData</structfield> is <literal>true</literal> then
-       <structfield>leafValue</structfield> must be set to the value of
-       <structname>spgConfigIn</structname>.<structfield>attType</structfield> type
+       <structfield>leafValue</structfield> must be set to the value (of type
+       <structname>spgConfigIn</structname>.<structfield>attType</structfield>)
        originally supplied to be indexed for this leaf tuple.  Also,
        <structfield>recheck</structfield> may be set to <literal>true</literal> if the match
        is uncertain and so the operator(s) must be re-applied to the actual
@@ -834,7 +846,7 @@ typedef struct spgLeafConsistentOut
    </variablelist>
 
  <para>
-  The optional user-defined method are:
+  The optional user-defined methods are:
  </para>
 
  <variablelist>
@@ -842,15 +854,22 @@ typedef struct spgLeafConsistentOut
      <term><function>Datum compress(Datum in)</function></term>
      <listitem>
       <para>
-       Converts the data item into a format suitable for physical storage in
-       a leaf tuple of index page.  It accepts
+       Converts a data item into a format suitable for physical storage in
+       a leaf tuple of the index.  It accepts a value of type
        <structname>spgConfigIn</structname>.<structfield>attType</structfield>
-       value and returns
-       <structname>spgConfigOut</structname>.<structfield>leafType</structfield>
-       value.  Output value should not be toasted.
+       and returns a value of type
+       <structname>spgConfigOut</structname>.<structfield>leafType</structfield>.
+       The output value must not contain an out-of-line TOAST pointer.
+      </para>
+
+      <para>
+       Note: the <function>compress</function> method is only applied to
+       values to be stored.  The consistent methods receive query scankeys
+       unchanged, without transformation using <function>compress</function>.
       </para>
      </listitem>
     </varlistentry>
+
     <varlistentry>
      <term><function>options</function></term>
      <listitem>
diff --git a/src/backend/access/spgist/spgscan.c b/src/backend/access/spgist/spgscan.c
index 20e67c3f7d..06011d2c02 100644
--- a/src/backend/access/spgist/spgscan.c
+++ b/src/backend/access/spgist/spgscan.c
@@ -81,7 +81,10 @@ pairingheap_SpGistSearchItem_cmp(const pairingheap_node *a,
 static void
 spgFreeSearchItem(SpGistScanOpaque so, SpGistSearchItem *item)
 {
-	if (!so->state.attLeafType.attbyval &&
+	/* value is of type attType if isLeaf, else of type attLeafType */
+	/* (no, that is not backwards; yes, it's confusing) */
+	if (!(item->isLeaf ? so->state.attType.attbyval :
+		  so->state.attLeafType.attbyval) &&
 		DatumGetPointer(item->value) != NULL)
 		pfree(DatumGetPointer(item->value));
 
@@ -296,6 +299,7 @@ spgbeginscan(Relation rel, int keysz, int orderbysz)
 {
 	IndexScanDesc scan;
 	SpGistScanOpaque so;
+	TupleDesc	outTupDesc;
 	int			i;
 
 	scan = RelationGetIndexScan(rel, keysz, orderbysz);
@@ -314,8 +318,21 @@ spgbeginscan(Relation rel, int keysz, int orderbysz)
 											 "SP-GiST traversal-value context",
 											 ALLOCSET_DEFAULT_SIZES);
 
-	/* Set up indexTupDesc and xs_hitupdesc in case it's an index-only scan */
-	so->indexTupDesc = scan->xs_hitupdesc = RelationGetDescr(rel);
+	/*
+	 * Set up indexTupDesc and xs_hitupdesc in case it's an index-only scan.
+	 * (It's rather annoying to do this work when it might be wasted, but for
+	 * most opclasses we can re-use the index reldesc instead of making one.)
+	 */
+	if (so->state.attType.type ==
+		TupleDescAttr(RelationGetDescr(rel), 0)->atttypid)
+		outTupDesc = RelationGetDescr(rel);
+	else
+	{
+		outTupDesc = CreateTemplateTupleDesc(1);
+		TupleDescInitEntry(outTupDesc, 1, NULL,
+						   so->state.attType.type, -1, 0);
+	}
+	so->indexTupDesc = scan->xs_hitupdesc = outTupDesc;
 
 	/* Allocate various arrays needed for order-by scans */
 	if (scan->numberOfOrderBys > 0)
@@ -447,9 +464,10 @@ spgNewHeapItem(SpGistScanOpaque so, int level, ItemPointer heapPtr,
 	item->level = level;
 	item->heapPtr = *heapPtr;
 	/* copy value to queue cxt out of tmp cxt */
+	/* caution: "leafValue" is of type attType not leafType */
 	item->value = isnull ? (Datum) 0 :
-		datumCopy(leafValue, so->state.attLeafType.attbyval,
-				  so->state.attLeafType.attlen);
+		datumCopy(leafValue, so->state.attType.attbyval,
+				  so->state.attType.attlen);
 	item->traversalValue = NULL;
 	item->isLeaf = true;
 	item->recheck = recheck;
@@ -497,6 +515,7 @@ spgLeafTest(SpGistScanOpaque so, SpGistSearchItem *item,
 		in.nkeys = so->numberOfKeys;
 		in.orderbys = so->orderByData;
 		in.norderbys = so->numberOfNonNullOrderBys;
+		Assert(!item->isLeaf);	/* else reconstructedValue would be wrong type */
 		in.reconstructedValue = item->value;
 		in.traversalValue = item->traversalValue;
 		in.level = item->level;
@@ -563,6 +582,7 @@ spgInitInnerConsistentIn(spgInnerConsistentIn *in,
 	in->orderbys = so->orderByData;
 	in->nkeys = so->numberOfKeys;
 	in->norderbys = so->numberOfNonNullOrderBys;
+	Assert(!item->isLeaf);		/* else reconstructedValue would be wrong type */
 	in->reconstructedValue = item->value;
 	in->traversalMemoryContext = so->traversalCxt;
 	in->traversalValue = item->traversalValue;
@@ -589,6 +609,7 @@ spgMakeInnerItem(SpGistScanOpaque so,
 		: parentItem->level;
 
 	/* Must copy value out of temp context */
+	/* (recall that reconstructed values are of type leafType) */
 	item->value = out->reconstructedValues
 		? datumCopy(out->reconstructedValues[i],
 					so->state.attLeafType.attbyval,
diff --git a/src/backend/access/spgist/spgutils.c b/src/backend/access/spgist/spgutils.c
index 949352ada7..cc5cacf624 100644
--- a/src/backend/access/spgist/spgutils.c
+++ b/src/backend/access/spgist/spgutils.c
@@ -23,6 +23,7 @@
 #include "access/xact.h"
 #include "catalog/pg_amop.h"
 #include "commands/vacuum.h"
+#include "nodes/nodeFuncs.h"
 #include "storage/bufmgr.h"
 #include "storage/indexfsm.h"
 #include "storage/lmgr.h"
@@ -53,7 +54,7 @@ spghandler(PG_FUNCTION_ARGS)
 	amroutine->amoptionalkey = true;
 	amroutine->amsearcharray = false;
 	amroutine->amsearchnulls = true;
-	amroutine->amstorage = false;
+	amroutine->amstorage = true;
 	amroutine->amclusterable = false;
 	amroutine->ampredlocks = false;
 	amroutine->amcanparallel = false;
@@ -89,6 +90,66 @@ spghandler(PG_FUNCTION_ARGS)
 	PG_RETURN_POINTER(amroutine);
 }
 
+/*
+ * GetIndexInputType
+ *		Determine the nominal input data type for an index column
+ *
+ * We define the "nominal" input type as the associated opclass's opcintype,
+ * or if that is a polymorphic type, the base type of the heap column or
+ * expression that is the index's input.  The reason for preferring the
+ * opcintype is that non-polymorphic opclasses probably don't want to hear
+ * about binary-compatible input types.  For instance, if a text opclass
+ * is being used with a varchar heap column, we want to report "text" not
+ * "varchar".  Likewise, opclasses don't want to hear about domain types,
+ * so if we do consult the actual input type, we make sure to flatten domains.
+ *
+ * At some point maybe this should go somewhere else, but it's not clear
+ * if any other index AMs have a use for it.
+ */
+static Oid
+GetIndexInputType(Relation index, AttrNumber indexcol)
+{
+	Oid			opcintype;
+	AttrNumber	heapcol;
+	List	   *indexprs;
+	ListCell   *indexpr_item;
+
+	Assert(index->rd_index != NULL);
+	Assert(indexcol > 0 && indexcol <= index->rd_index->indnkeyatts);
+	opcintype = index->rd_opcintype[indexcol - 1];
+	if (!IsPolymorphicType(opcintype))
+		return opcintype;
+	heapcol = index->rd_index->indkey.values[indexcol - 1];
+	if (heapcol != 0)			/* Simple index column? */
+		return getBaseType(get_atttype(index->rd_index->indrelid, heapcol));
+
+	/*
+	 * If the index expressions are already cached, skip calling
+	 * RelationGetIndexExpressions, as it will make a copy which is overkill.
+	 * We're not going to modify the trees, and we're not going to do anything
+	 * that would invalidate the relcache entry before we're done.
+	 */
+	if (index->rd_indexprs)
+		indexprs = index->rd_indexprs;
+	else
+		indexprs = RelationGetIndexExpressions(index);
+	indexpr_item = list_head(indexprs);
+	for (int i = 1; i <= index->rd_index->indnkeyatts; i++)
+	{
+		if (index->rd_index->indkey.values[i - 1] == 0)
+		{
+			/* expression column */
+			if (indexpr_item == NULL)
+				elog(ERROR, "wrong number of index expressions");
+			if (i == indexcol)
+				return getBaseType(exprType((Node *) lfirst(indexpr_item)));
+			indexpr_item = lnext(indexprs, indexpr_item);
+		}
+	}
+	elog(ERROR, "wrong number of index expressions");
+	return InvalidOid;			/* keep compiler quiet */
+}
+
 /* Fill in a SpGistTypeDesc struct with info about the specified data type */
 static void
 fillTypeDesc(SpGistTypeDesc *desc, Oid type)
@@ -109,6 +170,7 @@ spgGetCache(Relation index)
 	if (index->rd_amcache == NULL)
 	{
 		Oid			atttype;
+		Oid			indexatttype;
 		spgConfigIn in;
 		FmgrInfo   *procinfo;
 		Buffer		metabuffer;
@@ -121,11 +183,11 @@ spgGetCache(Relation index)
 		Assert(index->rd_att->natts == 1);
 
 		/*
-		 * Get the actual data type of the indexed column from the index
-		 * tupdesc.  We pass this to the opclass config function so that
+		 * Get the actual (well, nominal) data type of the column being
+		 * indexed.  We pass this to the opclass config function so that
 		 * polymorphic opclasses are possible.
 		 */
-		atttype = TupleDescAttr(index->rd_att, 0)->atttypid;
+		atttype = GetIndexInputType(index, 1);
 
 		/* Call the config function to get config info for the opclass */
 		in.attType = atttype;
@@ -136,18 +198,30 @@ spgGetCache(Relation index)
 						  PointerGetDatum(&in),
 						  PointerGetDatum(&cache->config));
 
+		/*
+		 * The leafType had better agree with the actual index column type,
+		 * which index.c will have derived from the opclass's opcintype.
+		 */
+		indexatttype = TupleDescAttr(RelationGetDescr(index), 0)->atttypid;
+		if (OidIsValid(cache->config.leafType) &&
+			cache->config.leafType != indexatttype)
+			ereport(ERROR,
+					(errcode(ERRCODE_INVALID_PARAMETER_VALUE),
+					 errmsg("SP-GiST leaf data type %s does not match declared type %s",
+							format_type_be(cache->config.leafType),
+							format_type_be(indexatttype))));
+
 		/* Get the information we need about each relevant datatype */
 		fillTypeDesc(&cache->attType, atttype);
 
-		if (OidIsValid(cache->config.leafType) &&
-			cache->config.leafType != atttype)
+		if (indexatttype != atttype)
 		{
 			if (!OidIsValid(index_getprocid(index, 1, SPGIST_COMPRESS_PROC)))
 				ereport(ERROR,
 						(errcode(ERRCODE_INVALID_PARAMETER_VALUE),
 						 errmsg("compress method must be defined when leaf type is different from input type")));
 
-			fillTypeDesc(&cache->attLeafType, cache->config.leafType);
+			fillTypeDesc(&cache->attLeafType, indexatttype);
 		}
 		else
 		{
diff --git a/src/backend/access/spgist/spgvalidate.c b/src/backend/access/spgist/spgvalidate.c
index 8bc3889a4d..b2f1ffa30f 100644
--- a/src/backend/access/spgist/spgvalidate.c
+++ b/src/backend/access/spgist/spgvalidate.c
@@ -43,6 +43,7 @@ spgvalidate(Oid opclassoid)
 	Form_pg_opclass classform;
 	Oid			opfamilyoid;
 	Oid			opcintype;
+	Oid			opckeytype;
 	char	   *opclassname;
 	HeapTuple	familytup;
 	Form_pg_opfamily familyform;
@@ -57,6 +58,7 @@ spgvalidate(Oid opclassoid)
 	spgConfigOut configOut;
 	Oid			configOutLefttype = InvalidOid;
 	Oid			configOutRighttype = InvalidOid;
+	Oid			configOutLeafType = InvalidOid;
 
 	/* Fetch opclass information */
 	classtup = SearchSysCache1(CLAOID, ObjectIdGetDatum(opclassoid));
@@ -66,6 +68,7 @@ spgvalidate(Oid opclassoid)
 
 	opfamilyoid = classform->opcfamily;
 	opcintype = classform->opcintype;
+	opckeytype = classform->opckeytype;
 	opclassname = NameStr(classform->opcname);
 
 	/* Fetch opfamily information */
@@ -118,13 +121,20 @@ spgvalidate(Oid opclassoid)
 				configOutLefttype = procform->amproclefttype;
 				configOutRighttype = procform->amprocrighttype;
 
+				/* Identify actual leaf datum type */
+				if (OidIsValid(configOut.leafType))
+					configOutLeafType = configOut.leafType;
+				else if (OidIsValid(opckeytype))
+					configOutLeafType = opckeytype;
+				else
+					configOutLeafType = procform->amproclefttype;
+
 				/*
 				 * When leaf and attribute types are the same, compress
 				 * function is not required and we set corresponding bit in
 				 * functionset for later group consistency check.
 				 */
-				if (!OidIsValid(configOut.leafType) ||
-					configOut.leafType == configIn.attType)
+				if (configOutLeafType == configIn.attType)
 				{
 					foreach(lc, grouplist)
 					{
@@ -156,7 +166,7 @@ spgvalidate(Oid opclassoid)
 					ok = false;
 				else
 					ok = check_amproc_signature(procform->amproc,
-												configOut.leafType, true,
+												configOutLeafType, true,
 												1, 1, procform->amproclefttype);
 				break;
 			case SPGIST_OPTIONS_PROC:
diff --git a/src/include/access/spgist_private.h b/src/include/access/spgist_private.h
index b6f95421d8..980aa7766b 100644
--- a/src/include/access/spgist_private.h
+++ b/src/include/access/spgist_private.h
@@ -151,8 +151,8 @@ typedef struct SpGistState
 typedef struct SpGistSearchItem
 {
 	pairingheap_node phNode;	/* pairing heap node */
-	Datum		value;			/* value reconstructed from parent or
-								 * leafValue if heaptuple */
+	Datum		value;			/* value reconstructed from parent, or
+								 * leafValue if isLeaf */
 	void	   *traversalValue; /* opclass-specific traverse value */
 	int			level;			/* level of items on this page */
 	ItemPointerData heapPtr;	/* heap info, if heap tuple */
@@ -208,7 +208,7 @@ typedef struct SpGistScanOpaqueData
 
 	/* These fields are only used in amgettuple scans: */
 	bool		want_itup;		/* are we reconstructing tuples? */
-	TupleDesc	indexTupDesc;	/* if so, tuple descriptor for them */
+	TupleDesc	indexTupDesc;	/* if so, descriptor for reconstructed tuples */
 	int			nPtrs;			/* number of TIDs found on current page */
 	int			iPtr;			/* index for scanning through same */
 	ItemPointerData heapPtrs[MaxIndexTuplesPerPage];	/* TIDs from cur page */
diff --git a/src/test/regress/expected/rangetypes.out b/src/test/regress/expected/rangetypes.out
index 05b882fde9..e6ca99d43d 100644
--- a/src/test/regress/expected/rangetypes.out
+++ b/src/test/regress/expected/rangetypes.out
@@ -1413,12 +1413,31 @@ RESET enable_bitmapscan;
 create table test_range_elem(i int4);
 create index test_range_elem_idx on test_range_elem (i);
 insert into test_range_elem select i from generate_series(1,100) i;
+SET enable_seqscan    = f;
 select count(*) from test_range_elem where i <@ int4range(10,50);
  count 
 -------
     40
 (1 row)
 
+-- also test spgist index on anyrange expression
+create index on test_range_elem using spgist(int4range(i,i+10));
+explain (costs off)
+select count(*) from test_range_elem where int4range(i,i+10) <@ int4range(10,30);
+                               QUERY PLAN                                
+-------------------------------------------------------------------------
+ Aggregate
+   ->  Index Scan using test_range_elem_int4range_idx on test_range_elem
+         Index Cond: (int4range(i, (i + 10)) <@ '[10,30)'::int4range)
+(3 rows)
+
+select count(*) from test_range_elem where int4range(i,i+10) <@ int4range(10,30);
+ count 
+-------
+    11
+(1 row)
+
+RESET enable_seqscan;
 drop table test_range_elem;
 --
 -- Btree_gist is not included by default, so to test exclusion
diff --git a/src/test/regress/sql/rangetypes.sql b/src/test/regress/sql/rangetypes.sql
index e1b8917c0c..cb5353de6f 100644
--- a/src/test/regress/sql/rangetypes.sql
+++ b/src/test/regress/sql/rangetypes.sql
@@ -375,8 +375,18 @@ create table test_range_elem(i int4);
 create index test_range_elem_idx on test_range_elem (i);
 insert into test_range_elem select i from generate_series(1,100) i;
 
+SET enable_seqscan    = f;
+
 select count(*) from test_range_elem where i <@ int4range(10,50);
 
+-- also test spgist index on anyrange expression
+create index on test_range_elem using spgist(int4range(i,i+10));
+explain (costs off)
+select count(*) from test_range_elem where int4range(i,i+10) <@ int4range(10,30);
+select count(*) from test_range_elem where int4range(i,i+10) <@ int4range(10,30);
+
+RESET enable_seqscan;
+
 drop table test_range_elem;
 
 --
