In standard Precise Point Positioning (PPP), the carrier phase ambiguities are estimated as real-valued constants, so that the carrier-phases can provide similar information as the pseudoranges. As a consequence, it can take tens of minutes to several hours for the ambiguities to converge to suitably precise values. Recently, new processing methods have been identified that permit the ambiguities to be estimated more appropriately as integer-valued constants, as they are in relative Real-Time Kinematic (RTK) positioning. Under these conditions, standard ambiguity resolution techniques can be applied to strengthen the PPP solution. The result can be a greatly reduced solution convergence and re-convergence period, representing a significant step toward improving the performance of PPP with respect to that of RTK processing. This paper describes the underlying principles of the method, why the enhancements work, and presents some results.