A new indexing method, called Compressed Multi-Framed Signature File (C-MFSF), that uses a partial query evaluation strategy with compressed signature bit slices is presented. In C-MFSF, a signature file is divided into variable sized compressed vertical frames with different on-bit densities to optimize the response time. Experiments with a real database of 152,850 records show that a response time less than 150 milliseconds is possible. For multi-term queries C-MFSF obtains the query results with fewer disk accesses than the inverted files. The method requires no indexing vocabulary. These attributes have important implications; for example, web search engines process multi-term queries in very large databases with sizeable vocabularies.