Accumulation of spectra is a common approach for improvement of the signal-to-noise ratio (SNR) in mass spectrometry. However, severe degradation of the overall spectrum can occur if some individual mass spectra, affected by peak broadening, are included in the accumulation process. In this contribution, we discuss potential sources and effects of spectral distortions by using examples from mass spectra acquired by our miniature laser ablation/ionisation time-of-flight mass spectrometer. We show how recent developments in acquisition systems enable to identify individual spectra subjected to peak broadening and present a filtering method capable of systematic and reproducible exclusion of such spectra from the accumulation process. We show that the method can be used on a wide range of materials and present a detailed case study performed on a trevorite mineral sample. Using this method, improvements of the isotope accuracy of Si, Ni, and Cr by factors between 1.6 and 7.7 were achieved. Finally, we discuss the limitations of the method and provide complementary analysis of other materials in the supplementary documents provided with this contribution.