Swimming pools in Madrid

I am flying to Madrid on Saturday (my first time in Spain! On my way to a SwimTrek vacation in the Canary islands!). It is my habit when flying from the East Coast to Europe to try to find a swimming pool to swim some laps as soon as I land. It's usually too early to check into the hotel, and this way I get to take a shower, change, get some exercise to wake up and generally shake off jet lag to keep me going on my first day in Europe.

Does anyone know of pools in Madrid where I might be able to drop in for some lap swimming? I have looked at the places2swim website, which has a number of ideas, but any real-world suggestions from people with first-hand experience would be welcome.

Thanks!

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