The stored waveform inverse Fourier transform (SWIFT) technique is used for broadband excitation of ions in an ion‐trap mass spectrometer to perform mass‐selective accumulation, isolation, and fragmentation of peptide ions formed by matrix‐assisted laser desorption/ionization. Unit mass resolution is achieved for isolation of ions in the range of m/z up to 1300 using a two‐step isolation technique with stretched‐in‐time narrow band SWIFT pulses at the second stage. The effect of "stretched‐in‐time' waveforms is similar to that observed previously for mass‐scan‐rate reduction. The asymmetry phenomenon resulting from the stretched ion‐trap electrode geometry is observed during application of normal and time‐reversed waveforms and is similar to the asymmetry effects observed for forward and reverse mass scans in the resonance ejection mode. Mass‐selective accumulation of ions from multiple laser shots was accomplished using a method described earlier that involves increasing the trapping voltage during ion introduction for more efficient trapping of ions.