Lorimer et al. have recently reported that the spin-down age (similar
to 7 x 10(9) yr) of the low-mass binary pulsar PSR J1012+5307 is much
higher than the cooling age (3 x 10(8) yr) of its white dwarf companio
n. The proposed solutions for this discrepancy are outlined and discus
sed. In particular, the revised cooling age estimate proposed by Alber
ts ct al. agrees with data from other low-mass binary pulsar systems i
f a transition to the 'classical' cooling regime occurs between simila
r to 0.14 and similar to 0.28 M.. If this transition is excluded, PSR
J1012+5307 seems to have finished its accretion phase far from the spi
n-up line.