We discuss the formation of pulsars with massive companions in eccentric or
bits. We demonstrate that the probability for a non-recycled radio pulsar t
o have a white dwarf as a companion is comparable to that of having an old
neutron star as a companion, Special emphasis is given to PSR B1820-11 and
PSR B2303+46. Based on population synthesis calculations we argue that PSR
B1820-11 and PSR B2303+46 could very well be accompanied by white dwarfs wi
th mass greater than or similar to 1.1M.. For PSR B1820-11, however, we can
not exclude the possibility that its companion is a main-sequence star with
a mass between similar to 0.7M. and similar to 5M..