Help with SQL

I'm new to postgres.
I've got 2 SQL statements I would like to combine into one.

I think I need to use a sub select or join I am not sure.
Any help would be appreciated!

statement 1: SELECT uid, count(uid) FROM triangulated WHERE uid != 'anonymus' AND uid
!= 'anonymous' AND uid != '' GROUP BY uid ORDER BY count DESC LIMIT 10;

that returns something like this:

uid | count
-------------+-------
eblevins | 1179
DaClyde | 398
Drew | 30
zombiechick | 3
(4 rows)

statement 2: SELECT uid, count(uid) FROM points WHERE uid != 'anonymus' AND uid !=
'anonymous' AND uid != '' GROUP BY uid ORDER BY count DESC LIMIT 10;

that returns something like this:
uid | count
-------------+-------
eblevins | 23595
DaClyde | 11031
zombiechick | 159
Drew | 104
(4 rows)

what I want to do is have one statement that returns something like this:
uid | count1 | count2
eblevins 1179 23595
DaClyde 398 11031
Drew 30 104
zombiechick 3 159

So everything is ordered like statement 1 but includes the count(uid) from the points DB like statement 2 returns

Any ideas on an effecient way of doing this?