Bad query plan with high-cardinality column

I have a problem with a query that is planned wrong. This is my schema:

create table comments (
id serial primary key,
conversation_id integer,
created_at timestamp
);
create index comments_conversation_id_index on comments (conversation_id);
create index comments_created_at_index on comments (created_at);

The table has 3.5M rows, and 650k unique values for "conversation_id", where the histogram goes up to 54000 rows for the most frequent ID, with a long tail. There are only 20 values with a frequency of 1000 or higher. The "created_at" column has 3.5M distinct values.

Now, I have this query:

select comments.id from comments where
conversation_id = 3975979 order by created_at limit 13

This filters about 5000 rows and returns the oldest 13 rows. But the query is consistently planned wrong:

Limit (cost=0.00..830.53 rows=13 width=12) (actual time=3174.862..3179.525 rows=13 loops=1)
Buffers: shared hit=2400709 read=338923 written=21
-> Index Scan using comments_created_at_index on comments (cost=0.00..359938.52 rows=5634 width=12) (actual time=3174.860..3179.518 rows=13 loops=1)
Filter: (conversation_id = 3975979)
Rows Removed by Filter: 2817751
Buffers: shared hit=2400709 read=338923 written=21
Total runtime: 3179.553 ms

It takes anywhere between 3 seconds and several minutes to run, depending on how warm the disk cache is. This is the correct plan and index usage:

Limit (cost=6214.34..6214.38 rows=13 width=12) (actual time=25.471..25.473 rows=13 loops=1)
Buffers: shared hit=197 read=4510
-> Sort (cost=6214.34..6228.02 rows=5471 width=12) (actual time=25.469..25.470 rows=13 loops=1)
Sort Key: created_at
Sort Method: top-N heapsort Memory: 25kB
Buffers: shared hit=197 read=4510
-> Index Scan using comments_conversation_id_index on comments (cost=0.00..6085.76 rows=5471 width=12) (actual time=1.163..23.955 rows=5834 loops=1)
Index Cond: (conversation_id = 3975979)
Buffers: shared hit=197 read=4510
Total runtime: 25.500 ms

The problem for Postgres is obviously to estimate how many rows have a given "conversation_id" value, but I have confirmed that the value is correctly tracked in the histogram.

I'm at a loss how to explain why the planner thinks scanning a huge index that covers the entire table will ever beat scanning a small index that has 17% of the table's values. Even if the entire database were in RAM, this would hit way too much buffers unnecessarily. (I have determined that planner will consistently use the bad plan for higher-frequency values, and the good plan for lower-frequency values.) It will *always* be better to branch off the "comments_conversation_id_index" index.

Another curious thing: If I run ANALYZE repeatedly, the planner will sometimes, oddly enough, choose the correct plan. This behaviour actually seems related to effective_cache_size; if it's set small (128MB), the planner will sometimes favour the good plan, but if large (>= 2GB) it will consistently use the bad plan. Not sure if ANALYZE is changing anything or if it's just bad timing.

Things I have tried: I have bumped the statistics target up to 10000, but it does not help. I have also tried setting n_distinct for the column manually, since Postgres guesses it's 285k instead of 650k, but that does not help.

Our environment: 9.2.2, tweaked memory parameters (work_mem, sort_mem, shared_buffers, effective_cache_size), not touched planner/cost parameters. Problem also exists on 9.2.3.