The self-similarmodel of coronal transients by B.C. Low is reconsidered. Due to a modification of the basic set of the initial assumptions of the model, a new class of more consistent solutions is found. The main advantage of these new solutions is that they do not contain areas with a physically inconsistent negative pressure. Instead, the novel solutions are derived on the basis of a special prescription for the thermal pressure of the transients that guarantees, by design, its positiveness throughout the whole evolution domain. The possible importance of these solutions for understanding the physics of the transient interplanetary coronal mass ejections (ICMEs; originating from the Sun), and magnetic clouds as a subclass of these, is discussed. A practical example is cited illustrating the application of our analytic results to describe some properties of real ICMEs. Some directions and scopes for further research are outlined.