blank subreports appearing on every record of report

[bicyclops]

I have a report with many records, and only on a few records there will be a
subreport displayed. This works fine, except that a little sliver of the
subreport shows up on every record of the report.
Each little sliver is blank, but adds a bit of height to each row, and
generally looks ugly.
I've set all of the 'Can Shrink' properties to yes, including the various
sections, controls, and subreport reference on the main report. All the
header & footer sections are zeroed out.

Isn't this what the 'Filter On Empty Master' property is supposed to do? It
has no effect.

Thanks in advance.