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We demonstrate how measuring orbital period derivatives can lead to moreaccurate distance estimates and transverse velocities for some nearby binarypulsars. In many cases this method will estimate distances more accurately thanis possible by annual parallax, as the relative error decreases as t^-5/2.Unfortunately, distance uncertainties limit the degree to which nearbyrelativistic binary pulsars can be used for testing the general relativisticprediction of orbital period decay to a few percent. Nevertheless, the measuredorbital period derivative of PSR B1534+12 agrees within the observationaluncertainties with that predicted by general relativity if the proper-motioncontribution is accounted for.Comment: 4 pages, latex, uuencoded compressed postscript + source, no figures,  uses aaspptwo.sty and dec.sty, accepted for publication in ApJL, omitted  reference now include

A New Method for Obtaining Binary Pulsar Distances and its Implications for Tests of General Relativity