Reliable estimation of earthquake source parameters is fundamental to improve our understanding of earthquake source physics and for ground‐motion modeling in seismic hazard assessment. Nowadays, methods traditionally used for investigating the source parameters of earthquakes with ≥3, such as spectral fitting or spectral ratio approaches, are also extensively applied to smaller magnitude events because of the increase in the number of stations and the more common borehole installations. However, when working with recordings of such minor and microearthquakes, significant limitations of the usable frequency range spanned by the spectra arise. At the lower end, signal‐to‐noise ratio constraints limit the usage of low frequencies, whereas at the upper end, the sampling rates of typical seismological networks as well as high‐frequency attenuation can be limiting factors. In addition, earthquake source parameters determined from ground‐motion spectra are known to exhibit potentially serious trade‐offs, in particular the corner frequency and high‐frequency attenuation. In this study, we go beyond the typical discussion of these trade‐offs using simplistic spectral models by investigating the impact of the background wave propagation model on the source parameter trade‐offs as well as its effect on the feasibility of obtaining useful source parameters by means of spectral fitting for minor and microevents. The analysis takes advantage of ad hoc simulated synthetic seismograms with well‐defined underlying background propagation models and considers increasing complications in these models (intrinsic and scattering attenuation). The results show that with given realistic background models and usable frequency bands, the source parameter estimation for minor and microevents can be significantly biased, and not surprisingly, this bias is mainly affecting the estimation of the corner frequency. We highlight the inherent limitations of joint spectral fitting approaches for the determination of source parameters from minor and microearthquakes, which should always be viewed with great caution when physically interpreted.