As I recall, three things to consider to understand storm strength:

* Winds, which are directly related to current central core strength.
* Size, which is completely independent of anything but size and windfield diameter.
* Storm surge, which is a combination of current central pressure and past central pressure.

It is storm surge which is most effected by a storm that was previously strong, since it often takes time for the surge to subside away from a storm when the pressure rises, just as it takes time for the surge to build when the pressure falls.

Hope this helps