Styling a table cell to be a "spring"

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CSS

HTML

I have a table that displays information on break-out sessions for my company's upcoming annual meeting, rooms along the side and time periods along the top. Each cell in that table contains an inner table with information for each particular session; the inner table has three rows of one cell each.

I would like to get the bottom row of the inner table to align with the bottom of the cell in the outer table, while keeping the top row of the inner table aligned with the top of the outer cell.

I would think I could style the middle cell to be a "spring", ie take up as much vertical space as possible. I have tried using height:100% ! important; on both the middle cell of the inner table and on the inner table itself, but neither seem to make any difference. I feel like I'm missing something that is blatantly obvious.

Any suggestions?

If it makes any difference, the page is XHTML Strict.