  We present transport measurements of unshunted dc superconducting quantum
interference devices (SQUIDs) consisting of 30 nm wide aluminum nanobridges of
varying length L contacted with two and three dimensional banks. 3D nanobridge
SQUIDs with L $\leq$ 150 nm (approximately 3-4 times the superconducting
coherence length) exhibit $\approx 70%$ critical current modulation with
applied magnetic field, approaching the theoretical limit for an ideal short
metallic weak link. In contrast, 2D nanobridge SQUIDs exhibit significantly
lower critical current modulation. This enhanced nonlinearity makes 3D
nanobridge Josephson junctions well suited to optimize sensitivity in weak link
SQUID magnetometers as well as realize ultra low-noise amplifiers and qubits.
