The role of the saturable absorber dye DDI in the cw passively mode-locked Ti:sapphire/DDI laser both with and without compensation prisms is investigated. This laser self-starts when the concentration of the dye is greater than ≈2 × 10−4 M for both picosecond and femtosecond pulses. With the prism pair, the laser generates Gaussian pulses 150 fs in duration. The corresponding spectrum is sech2 in shape with a FWHM of 8 nm. These parameters are independent of the DDI concentration. Without the prism pair, the laser generates picosecond pulses with the FWHM decreasing from 8 to 3 ps as the dye concentration is increased from 2.5 × 10−4 to 1 × 10−3 M. Concurrently the pulse shape changes from a Lorentzian to a nearly symmetric two-sided exponential shape. The picosecond spectra for different dye concentrations are also presented.