COUNTIF and arrays?

This seems like it should be very simple, but the solution has evaded me the last few days.

Basically, I have huge amounts of data (tens of thousands of rows) that include dates and times. I'd like to simply count the rows of data between certain date ranges, e.g. how many rows of data fall between 7/1/2012 and 7/8/2012? I've considered using COUNTIF with an array of some sort, but I haven't had any luck so far. My best guess at a formula has been:

=COUNTIF(C:C,AND(C:C>=DATE(2012,7,1),C:C<=DATE(2012,7,7)=TRUE))

I've tried both as an array and not, as well as tossing in INDEX() nested within the AND() formula. All instances have produced a result of 0 (there should be 156).

Again, I know it should be simple, but it's lost on me. Any help would be greatly appreciated.

If you have XL2007 or 2010, try:

=COUNTIFS(C:C,">="&DATE(2012,7,1),C:C,"<="&DATE(2012,7,7))

else.

=COUNTIF(C:C,">="&DATE(2012,7,1))-COUNTIF(C:C,">"&DATE(2012,7,7))

Ah! I knew there was a simple solution. Thanks for humoring me, guys. That did the trick. =)