An experiment was performed using two cw Ar-ion lasers in Fabry-Perot resonators configured in a Ushaped cavity and coupled through a common end mirror to examine the effect of coupling strength on phase locking. The near field fringe visibilities were measured while varying the reflectivity of the common end mirror from 10% to 90%. Along with the total multiline visibility, the visibilities for single lines at 514.5 nm and 488.0 nm during multiline coupling were also measured. The lasers were also operated on a single line (488.0 nm), and measurements were made on single-line coupling. An RF mode beat at the frequency characteristic of the super cavity was observed for all values of coupling strength. The optimal coupling strength for phase-locked operation for Ar-ion lasers was found to be approximately 25%.