different sort order for primary key index

I have a composite primary key for a table, let's call it (col1, col2).
When this table is created, obviously an implicit index is created for this
key. I would like the sort order of this index to be different for the two
columns -- if I were to create the index myself, I would pass on (col1, col2
DESC). The ALTER INDEX documentation suggests that it's not possible to
change the sort order of a column, so I can envision two ways to get around
this: 1) create a second UNIQUE index of (col1, col2 DESC), or 2) not
define a primary key and just specify a UNIQUE index separately. Primary
keys are basically restricted to being unique and non-null, but I'm unclear
if PostgreSQL treats primary keys differently from unique, non-null
constraints.