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"if you think it wont offend your significant other, ask them where it was purchased from, we might be able to tell you more about it"

+1 to this

Oh and forgot you can strop a sharp blade on newspaper to keep the edge crisp. If you look in the wiki I think there is a thread about it.

Well as has been said different strops act differently. If your strop is a Illinois strop then it seeming stiff would be normal. But the flip side of that if it is a strop like a selective strop it...

Who makes the strop you have? Will be able to tell you much more with that information.