Work on projection-based induction of cross-lingual word embedding spaces (CLWEs) predominantly focuses on the improvement of the projection (i.e., mapping) mechanisms. In this work, in contrast, we show that a simple method for post-processing monolingual embedding spaces facilitates learning of the cross-lingual alignment and, in turn, substantially improves bilingual lexicon induction (BLI). The post-processing method we examine is grounded in the generalisation of first- and second-order monolingual similarities to the nth-order similarity. By post-processing monolingual spaces before the cross-lingual alignment, the method can be coupled with any projection-based method for inducing CLWE spaces. We demonstrate the effectiveness of this simple monolingual post-processing across a set of 15 typologically diverse languages (i.e., 15*14 BLI setups), and in combination with two different projection methods.