In an effort to greatly improve the measurement precision of VLBI observables used to determine geodetic baselines, the potential of utilizing fringe phase has been investigated. The 245-km baseline between Mojave and Owens Valley (in CA) has been most thoroughly studied for this purpose. In trying several different experimental designs it appears that source scheduling is not the critical factor in determining when phase connection can be established. Normally, instrumental instabilities are also not limiting (although nominal functioning of the instrumentation is essential). The most serious factor in limiting opportunities for phase connection seems to be atmospheric variability. However, when the observation SNR is made large (> 50) to give very precise group delays (and hence enhance the chance of resolving phase ambiguities), the improvement in baseline uncertainty obtained using phase delays is only marginal compared with the corresponding group delay solution. For this case, the baseline error budget is dominated by stochastic variations in clock and atmospheric delay contributions rather than by observation noise.