Counting data in non blank cells and exclude certain data from the count

Hopefully I can make myself clear with this one!

I am currently using the COUNTA formula to count non blank cells for a specific range but need to if possible to exclude from the count cells that contain specific data as well a blank data.

I'll try and explain!

The data I wish to exlude in the count are cells that are blank AND contain either Block, Not AM or Not PM

Eg:
Cell A1 = John
Cell A2 = Block
Cell A3 = Not AM
Cell A4 = Graham
Cell A5 is blank (no data)
Cell A6 = Sue
Cell A7 = Not PM

I need a formaular that will look at cells A1:A7 and will return the figure 3 as in my example (i.e. A1 as it contains John, A4 as it contains Graham and Cell A6 as it contains Sue as the other 4 are either blank or contain Block, Not AM or Not PM.

Hope this is clear and any help will be very much appriciated.

Many thanks
John

Another way...

=SUMPRODUCT(--(A1:A7<>""),--ISNA(MATCH(A1:A7,{"Block","Not AM","Not PM"},0)))

Thank you very much to both of you.

It's easy when you know how!