We present two analytical models of gravitational collapse toward the Schwarzschild black hole, starting from the interior of the revisited Schwarzschild solution recently reported [Phys. Rev. D 109, 104032 (2024)]. Both models satisfy some energy conditions at all times as long as the collapse is slower than some limit. While a singularity of the Schwarzschild black hole at the origin (R mu nu alpha beta R mu nu alpha beta similar to r-6) forms immediately after the start of the collapse in one model, such a singularity never appears at finite time during the collapse (except t -> infinity) in the other model. The scheme used shows great potential for studying in detail the appearance of singularities in general relativity.