I bought the specified replacement valve seal part 697338 but it is too loose and about 1mm in diameter smaller than the old one, and a different shape. It is engine model 126M02-1525-F1 for a craftsman lawn mower. I am the original owner. Any ideas on how to find a valve seal that fits, or why it would be different than specified?

I'm seeing a different part # altogether ( 590410 ):
 
https://www.partstree.com/models/126m02-1525-f1-briggs-stratton-vertical-engine/camshaft-crankshaft-cylinder-engine-sump-lubrication-pistion-group-valves-3/ 
 
 
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Thanks. I’ll give it a try and let you know.

The part you recommended fits, but now I need to figure out which direction to insert it. Either concave side down toward crankcase, or up toward valve seat. Any thoughts?

Here ya go: