In the field of structural analysis dedicated to the study of vibrations of high-speed railway bridges, one reference load model is the well-known HSLM-A, which limits of validity are stated in Eurocode EN 1991-2, Annex E. In a recent paper published in the Journal of Rail and Rapid Transit, the authors investigated the degree of coverage provided by HSLM-A to critical articulated trains. Now in the present article, the authors have extended those analyses to critical conventional and regular trains as well. This is an important aspect because HSLM-A as such is an articulated-type model, so it is of interest to understand how it deals with covering the various resonance phenomena generated by other train types. Therefore, the main goal of this work is to establish whether the conventional and regular trains that stem from the validity rules given in Annex E/EN 1991-2, produce vibratory effects that are duly covered by HSLM-A. Following the aforementioned validity rules, one first aspect analysed is the importance of near-to-integer wheelbase ratios in the coupled vibrations produced by conventional trains. Subsequently, seven realistic, conventional and regular high-speed train models have been synthesised; these models have been made publicly available in Mendeley Data, and comprise almost 3800 different sequences of axle loads. Finally, the response of simply-supported bridges has been analysed with a view to compare the seven synthesised models versus HSLM-A. The exceedance and required speed increase have been computed for both displacements and accelerations, in a comprehensive ensemble of spans and speeds. The results provide a diagnosis of the degree of coverage of HSLM-A with respect to those conventional and regular trains compliant with Annex E/EN 1991-2.