I have a Timex Expedition (men's) with an analog face and the digital window at the 6 o'clock position. I've swum in it lots of times with the chrono running, and it works great. I've also accidentally put it through the washing machine. Got it for $14 through Camp-Mor.
I have noticed that the men's watch handles water much better than my women's Expedition. The women's never sealed quite right after the battery was changed. (But it still worked. I got tired of pulling the back off and leaving it out to dry, though.)
Replaced the Timex strap with a Silverfoot mini-clip strap ($8). Very comfortable.
All my watches for the last 20 years or so (except my diving watch, which died a miserable salty death) have been Timexes. Usually various styles of Expedition. There are different water-resistance ratings. If you still have the one that leaked, try contacting Timex for a replacement.
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