TALP is a new direct-space strategy for ab initio crystal structure determination of molecular crystals from powder diffraction data. The strategy is based on a preliminary exploration stage, which considers atomic overlap, followed by a subsequent stage of local incremental scans, both coupled to fast restrained least-squares minimizations with the atomic coordinates as refined parameters. The observed intensities are extracted from the powder pattern by a three-step procedure [Vallcorba, Rius, Frontera, Peral & Miravitlles (2012). J. Appl. Cryst. 45, 844-848], and the molecular model and distance restraints are derived from molecular mechanics calculations or from similar reported structures. The solution process consists of several independent trials, each one resulting in a crystal structure proposal with an associated figure of merit. TALP has been tested on laboratory X-ray powder diffraction data of 14 molecular compounds of known crystal structure and of variable complexity. In most cases, the crystal structure is solved in a short time (less than an hour), even for calculated models. For the most complex structures (e.g. 13 torsion angles), the general scan is assisted by a rotation function, which provides a ranked list of most probable model orientations. In this way only the positional and conformation parameters need to be explored.