Thomas, I apologize for not providing more detail. The dataset and
model I was testing with are too complex and large to offer a test
case, and I thought you may already be aware of this.

In any case, I was am to reproduce this, using the JSP (for
convenience) code below; it just scans a large tree of directories to
create the test data. Otherwise I'm certain you can use *any* other
dataset once loaded into both h2 and pg.

http://kensystem.com/h2loader.txt

and run:
SELECT * FROM tbl WHERE val='/share/pictures/DCP_1303.JPG'

I have about 500,000 rows in both pg and h2; the time to execute is
about 1/3 on h2. Using Sun JRE 6x on 32bit/1386 Linux, running both
h2-1.2.130 and PG 8.3.

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