We compute the quark-antiquark potential in three-dimensional massive quant
um electrodynamics for an arbitrary fermion mass. The result indicates that
screening prevails for any quark masses, contrary to the classical expecta
tions, generalizing our previous result obtained for large masses. We also
test the validity of several approximation schemes using a detailed numeric
al analysis. The classical result is still reproduced for a small separatio
n of the quarks.