We present a new algorithm for the enumeration of chemical fragment spaces under constraints. Fragment spaces consist of a set of molecular fragments and a set of rules that specifies how fragments can be combined. Although fragment spaces typically cover an infinite number of molecules, they can be enumerated in case that a physicochemical profile of the requested compounds is given. By using min-max ranges for a number of corresponding properties, our algorithm is able to enumerate all molecules which obey these properties. To speed up the calculation, the given ranges are used directly during the build-up process to guide the selection of fragments. Furthermore, a topology based fragment filter is used to skip most of the redundant fragment combinations. We applied the algorithm to 40 different target classes. For each of these, we generated tailored fragment spaces from sets of known inhibitors and additionally derived ranges for several physicochemical properties. We characterized the target-specific fragment spaces and were able to enumerate the complete chemical subspaces for most of the targets.