One key part of the numerical solution of fluid-driven fracture propagation is the logic adopted to advance the fracture front during one time step. This is typically obtained by satisfying a quasi-static propagation condition. In this contribution, within the scope of a fully implicit scheme for mode I hydraulic fractures, we compare the use of either i) cohesive zone models, ii) the clas-sical linear elastic fracture mechanics energy condition or, iii) the complete hydraulic fracture tip asymptotics to advance the fracture tips. Thanks to semi-analytical solutions available for the case of both plane-strain and axisymmetric mode I hydraulic fractures, we can study the rate of conver-gence of the di˙erent propagation scheme toward the corresponding analytical solution (fracture length versus time, width versus time, pressure versus time). We clarify the requirements needed to achieve superior convergence rate and also discuss the impact of the di˙erent propagation scheme on computational robustness and performance.