This paper undertakes tracing down the semantic changes of the Hungarian preverb 'be' ('in') in the theoretical framework and with the methods the author set up during a similar discussion of the preverb 'ki' ('out'). This means, practically speaking, that she amalgamates the relevant syntactic and semantic aspects with a cognitively-based classification of arguments of the 'where to' type that can be considered a primary argument type of verbs combined with 'be,' as well as with a description of conceptualisation processes involving those arguments. As is revealed by Table 1 summarising the results of this investigation, the semantic bleaching of the preverb 'be' is due to processes at two levels that are interrelated and follow from one another. On the one hand, we have to do with a series of linearly linked changes from group A, standing for increasingly abstract representations of three-dimensional IN places, to group B that involves no characteristics of 'internal space' at all. On the other hand, however, within the various subtypes of internal spaces, a number of events may have occurred that resulted in a perfectivising role of the preverb and its various Aktionsart-forming functions. The description of changes involving illative landmark and trajectory functions reveals that the frequency of those events, their grammatical quality and the subsequent modification of directional meanings depend on the degree of abstraction and conceptualisation of IN places.