There exists an inherent difficulty in the original algorithm for the construction of Dwarf, which prevents it from constructing true Dwarfs. We explained when and why it introduces suffix redundancies into the Dwarf structure. To solve this problem, we proposed a completely new algorithm called PID. It bottom-up computes partitions of a fact table, and inserts them into the Dwarf structure. Ifa partition is an MSV partition, coalesce its sub-Dwarf; otherwise create necessary nodes and cells. Our performance study showed that PID is efficient. For further condensing of Dwarf, we proposed Condensed Dwarf, a more compressed structure, combining the strength of Dwarf and Condensed Cube. By eliminating unnecessary stores of "ALL" cells from the Dwarf structure, Condensed Dwarf could effectively reduce the size of Dwarf, especially for Dwarfs of the real world, which was illustrated by our experiments. Its query processing is still simple and, only two minor modifications to PID are required for the construction of Condensed Dwarf.