Disclosed are novel rigidified compounds having a rhodanine-like residue and at least one aryl or heteroaryl residue linked to the rhodanine-like residue, whereby a core structure of these compounds, as defined in the specification, is characterized as having one or zero free-to-rotate bonds. Also disclosed are pharmaceutical compositions containing these rigidified compounds and uses thereof for modulating the activity of heparanase and hence in the treatment of heparanase-associated diseases and disorders, and uses thereof for modulating the activity of heparin-binding proteins and hence in the treatment of heparin-binding proteins-associated diseases and disorders as well as in the treatment of medical conditions that are at least partially treatable by rhodanine or a rhodanine analog.