countif or sumproduct?

Using the following formula I can count the number of invoices which contain the data in cell 'M1' which happens to be an 'x' in this case.

=COUNTIF(F16:F1204,M1)

However, i need to add another criteria - i need to be able to count the number of invoices within the data range F16:F1204 which contain the same data as in cell M1 but also only to count the number of invoices within this range which DO NOT contain the phrase "Paid Account" in the corresponding cells of the data range J16:J1204

I'm not sure whether I can include multiple criteria in a countif function or whether I have to use a SUMPRODUCT formula, and if so, how??

Any help would be much appreciated.

Excellent! That works fine thanks, I can now amend the formula for the other similar things I need.