  A unified strategy is developed that can be used to search for millisecond
pulsars (MSPs) with ~solar mass companions (including neutron star companions
in double neutron star binaries [DNSBs]) belonging to both very short period
binaries, and those with periods so long that they could be appropriate targets
for acceleration searches, and to bridge the gap between these two extremes. In
all cases, the orbits are assumed to be circular. Applications to searches for
binary pulsars similar to PSR J0737-3039 are discussed. The most likely
candidates for more DNSBs consist of weakly magnetized neutron stars, spinning
only moderately fast, like J0737-3039A, with periods generally longer than 15
ms, though this issue is not yet settled. Because of the similarity between the
MSP components of DNSBs, and the longer period MSP population specific to
massive condensed or core collapsed globular clusters, as well as the
uncertainties about accretion-driven spinup, doubts linger about the standard
models of DNSB formation.
