  We discuss the formation of pulsars with massive companions in eccentric
orbits. We demonstrate that the probability for a non-recycled radio pulsar to
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 with mass >
1.1Msun. For PSR B1820-11, however, we can not exclude the possibility that its
companion is a main-sequence star with a mass between about 0.7Msun and 5Msun.
