This paper considers digital, IIR bandpass filters with adjustable bandwidth and centre frequency obtained from a lowpass prototype filter through lowpass-to-bandpass frequency transformations. Starting with a set of filter specifications, including requirements on passband and stopband edges as well as on passband and stopband ripples, it is shown how to select a lowpass prototype filter and how to perform the frequency transformations so as to ensure that all specifications are satisfied. Traditionally, only the passband (stopband) edges are controlled whereas one accepts the resulting stopband (passband) edges after the transformation, regardless their values.