In two previous papers, algorithms designed for searching, matching and identifying phases in qualitative X-ray powder analysis were reported [Schreiner, Surdukowski & Jenkins (1982). J. Appl. Cryst. 15,[513][514][515][516][517][518][519][520][521][522][523][524][525][526][527][528][529][530]. This paper extends the searching technique to unknowns containing isotypical phases and solid solutions. Methods are described for distinguishing among isotypical compounds in qualitative analyses, and for permitting the retrieval of phases in a data base that differ from measured patterns by a uniform Ad/d scale factor.