While edge pinning is known to play an important role in sub-$\ensuremath{\mu}\mathrm{m}$ wires, we demonstrate that strong deviations from the universal creep law can occur in 1 to $20\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{m}$ wide wires. Magnetic imaging shows that edge pinning translates into a marked bending of domain walls at low drive and is found to depend on the wire fabrication process and aging. Edge pinning introduces a reduction of domain wall velocity with respect to full films which increasingly dominates the creep dynamics as the wire width decreases. We show that the deviations from the creep law can be described by a simple model including a counter magnetic field which links the width of the wire to the edge dependent pinning strength. This counter field defines a key nonuniversal contribution to creep motion in patterned structures.