Trilateration surveys of a geodetic network across the Rio Grande rift near Socorro, New Mexico, in 1972, 1973, 1976, and 1979 have failed to detect any significant strain accumultion. The surveys place an upper bound (95% confidence limit) of 1 mm/a (a=years) on east-west spreading across the rift in 1972--1979. There is marginal evidence from triangulation for an episode of east-west spreading across the rift within the interval 1954--1972. The trilateration network lies on the south flank of an uplift caused by magma intrusion into a midcrustal sill during this century according to Reilinger and Oliver. The horizontal deformation induced by sill inflation is sufficiently small that continued uplift during 1972--1979 cannot be excluded by the observed of signficant horizontal deformation.