CountIf - Counting cells between a range of numbers

I am sure I'm missing something obvious, but I don't know what. I am interested in using the countif function to count the number of cells that fall between a certain time frame (i.e. 12/1/03 and 12/31/03) I can not figure out how to write a formula for "between". Any suggestions?

One more thought. Is it possible to write a formula as mentioned above, that would begin to recalculate at the start of a new month?

Thanks for the help!

matt

Thank you guys, your information was very thorough. If I may, there is a twist to consider. Column B has the Start Date.
I want to tally all of the dates in Column B that are greater than 12/10/3 and less than 12/31/03. This may be a stupid question but can I put in these fixed values instead of a cell reference?

Last piece of the pie. Is there a way within regular Excel to set up a "Case" statement. Thing is, I want to count the number of instances of a date that falls between the first and last date of the month, EVERY MONTH. So I could set up a column that will have January - December listed in it and a "Case" statement that would look at the start date and add it to the CountIf statement for the appropriate month. OR - Do I have to write the formula in each cell that I am looking for this data in?

Thanks for the help, again!

matt