Counting with a referenced "or" criteria

Hi all,

I'd like to count a simple table, based on 2 criteria:

1) If column "C" contains the letter "X"
2) If column "H" contains EITHER text entered into U2, or U3.

For other formulas that didn't require the "OR" condition, I've used either of these:
=COUNTIFS($H:$H,$U$2,$C:$C,"X*")
=SUMPRODUCT(--($H:$H=$U$2),--ISNUMBER(SEARCH("X",C:C,1)))

I also know there's the option of adding formulas together for each "OR" condition, such as:
=COUNTIFS($H:$H,$U$2,$C:$C,"X*")+COUNTIFS($H:$H,$U$3,$C:$C,"X*")

Is there a condensed formula (either countifs or sumproduct) that can count based on a referenced OR statement? The following doesn't work, but it's what I conceptually started with:
=COUNTIFS($H:$H,{"$U$2","$U$3"},$C:$C,"X*")

Try

=SUMPRODUCT(COUNTIFS($C:$C,"X*",$H:$H,$U$2:$U$3))