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Default Referencing previous column in COUNTIF

Evening All,

I am a novice Excel user, so please excuse the probably very basic
question. I have a spreadsheet with two columns, e.g.

A E
D E
F L
A E
G E

I am trying to get some totals for column 2 based on the value, so I
used COUNTIF(D4:D34, "E"). This is great, but I only want to count
column 2 if the corresponding cell in column 1 is "A" (or not "A" for
my other total). I think I want to somehow use INDIRECT as well, but
can't quite figure out how! The total I am looking for in the example
would be 2 (col2="E" and col1="A").

Thanks for any hints/advice.

Cheers,
Al.