Would You Trade Memory for Intelligence?

I often am surprised at how the human mind works.  The lady that sits in the cubicle across from mine often listens to the classic rock radio station, so when I'm not listening to my iPod, I'll just sit there and listen to whatever happens to pop up on that channel.  Anyway, today a song that I probably haven't heard in 15 or 20 years, "Can't Get It Out of My Head" by Electric Light Orchestra, comes on, and surprisingly (and probably embarrassingly) I remembered all of the words and various other idiosyncracies about the song (remembered how the string part here went, how the piano part there goes, etc.).

By now, you're probably asking yourself what this has to do with my being surprised at how the mind works.  Well, it got me to thinking - this is a song that I haven't heard in years, and I remembered that much about it.  Then I got to thinking about the bigger picture - you can easily multiply that by hundreds of thousands (or possibly millions) when you think about all the lyrics and music to all songs you've got sitting around in your brain.  Wasted space some people might call it.  I know that in general, different parts of your brain are used to store away & retrieve information (be song lyrics or the memory of your 5th birthday party) than perform complex thought/analysis, but if we could just tap into all that storage space stowing away the lyrics to "Unskinny Bop", maybe those cures for cancer wouldn't be so elusive. 

I know that science has proven that there are many areas of your brain that either really aren't doing anything or control involuntary functions, but let's say for the sake of argument that increasing capacity for complex thought/intelligence would be at the expense of real estate that could be used to retain memories. What do you think - would you be willing to sacrifice "memory storage space" in your brain for the ability to perform more complex thought (essentially trading memory for intelligence)?  What if you had no way to decide what memories were kept and which ones were "overwritten"?  Would you risk potentially "overwriting" your happy memories in order to gain some IQ points?  I know these questions are subjective - for many, it would depend on how much memory could be lost versus how much intelligence could be gained.  Just curious...