Problem resizing DB Grid with Columns enabled

Hello all.

I am trying to give users the ability to resize a DB grid and save the
resize settings to a database so users will see the grid resized the same
way every time they run our app.

To do this, I am converting our existing DB Grid and adding TDBGridColumns
for each DB field (there are 7).  I am saving the value of
DBGrid1.Columns[n].Width to the database for each field.

This grid might have multiple rows, so I am setting RowSelect to true.  Here
is the problem.  If the user resizes the 8 fields so they fit exactly in the
grid, the RowSelect fails-- users click on a cell and that cell is
highlighted, not the entire row.  If they resize the grid so that it is one
pixel from fitting exactly in the grid (say, DBGrid1.Columns[0].Width is
reduced by 1), I get the RowSelect capability back.

Any ideas as to how I can have a normal RowSelect capability for the "exact
fit" scenario?

Thanks in advance.
-Mike