ABSTRACT We investigate the relative strengths of classes of computation models using the 'While' programming language over many sorted algebras. We consider the 'While' language with and without counters, stacks and arrays; and also the language with a limited number of these constructs. Among the results we show are: * 'While' with 1 stack is incomparable with 'While' with counters; * 'While' with 2 counters (only) is as strong as 'While' with arbitrarily many counters; but * 'While' with 1 counter (only) is no stronger than 'While' without counters.