We have applied mechanical strain to mesoscopic Bi wires, and report several new observations, The universal conductance fluctuations (UCF) are quite sensitive to strain: a strain of only 5 x 10(-7) changes the conductance by order e(2)/h at T = 45 mK, suggesting a large shift with strain of either the Fermi energy or the positions of some scattering centers. The random telegraph signals associated with two-level systems (TLS) vary both in amplitude and switching rate with applied strain. The amplitude variation is random, consistent with UCF, while the slower transition rate varies monotonically with strain. The energy asymmetry of the TLS (deduced from the ratio of the transition rates) has a linear coupling to strain, with a deformation potential of 2-3 eV.