I discuss the relation between canonical and microcanonical analyses o
f first-order phase transitions. In particular it is shown that the mi
crocanonical Maxwell construction is equivalent to the equal-peak-heig
ht criterion often employed in canonical simulations. As a consequence
the microcanonical finite-size estimators for the transition point, l
atent heat and interface tension are identical to standard estimators
in the canonical ensemble. Special emphasis is placed on various ways
for estimating interface tensions. The theoretical considerations are
illustrated with numerical data for the two-dimensional 10-state Potts
model.