  We give a necessary, and in some cases sufficient, condition for sliceness
inside the family of pretzel knots $P (p_1,...,p_n)$ with one $p_i$ even. The
three stranded case yields two interesting families of examples: the first
consists of knots for which the non-sliceness is detected by the Alexander
polynomial while several modern obstructions to sliceness vanish. The second
family has the property that the correction terms from Heegaard-Floer homology
of the double branched covers of these knots do not obstruct the existence of a
rational homology ball; however, the Casson-Gordon invariants show that the
double branched covers do not bound rational homology balls.
