Self-assembled nanostructures and their stimuli-responsive degradation have been recently explored to meet the increasing need for advanced biocompatible and biodegradable materials for various biomedical applications. Incorporation of enzymes as triggers that can stimulate the degradation and disassembly of polymeric assemblies may be highly advantageous owing to their high selectivity and natural abundance in all living organisms. One of the key factors to consider when designing enzyme-responsive polymers is the ability to fine-tune the sensitivity of the platform toward its target enzyme in order to control the disassembly rate. In this work, a series of enzyme-responsive amphiphilic PEG-dendron hybrids with increasing number of hydrophobic cleavable end-groups was synthesized, characterized, and compared. These hybrids were shown to self-assemble in aqueous media into nanosized polymeric micelles, which could encapsulate small hydrophobic guests in their cores and release them upon enzymatic stimulus. Utilization of dendritic scaffolds as the responsive blocks granted ultimate control over the number of enzymatically cleavable end-groups. Remarkably, as we increased the number of end-groups, the micellar stability increased significantly and the range of enzymatic sensitivity spanned from highly responsive micelles to practically nondegradable ones. The reported results highlight the remarkable role of hydrophobicity in determining the micellar stability toward enzymatic degradation and its great sensitivity to small structural changes of the hydrophobic block, which govern the accessibility of the cleavable hydrophobic groups to the activating enzyme.