The neutron-deficient isotopes /sup 189-194/Tl have been studied using collinear fast atom beam laser spectroscopy with mass-separated beams of 7 x 10/sup 4/ to 4 x 10/sup 5/ atoms per second. By laser excitation of the 535 nm atomic transitions of atoms in the beam, the 6s/sup 2/7s /sup 2/S/sub 1/2/ and 6s/sup 2/6p /sup 2/P/sub 3/2/ hyperfine structures were measured, as were the isotope shifts of the 535 nm transitions. From these, the magnetic dipole moments, spectroscopic quadrupole moments, and isotopic changes in mean-square charge radii were deduced. A large isomer shift in /sup 193/Tl was observed, implying a larger deformation in the (9/2/sup -/ isomer than in the (1/2/sup +/ ground state. The /sup 189,191,193/Tl/sup m/ isotopes have deformations that increase as the mass decreases. A deformed shell model calculation indicates that this increase in deformation can account for the drop in energy of the (9/2/sup -/ bandhead in these isotopes. An increase in neutron pairing correlations, having opposite and compensating effects on the rotational moment of inertia, maintains the spacing of the levels in the (9/2/sup -/ strong-coupled band. Results for /sup 194/Tl/sup m/ differ from previously published values, but are consistent with the /sup 190,192/Tl/sup m/more » data.« less