We analyze the dynamics of mode-locked pumped solid-state lasers focusing on the transition between mode-locked and CW behavior. Where the ratio of the pump and laser cavity lengths is a rational number, 'rational-harmonic mode-locking' is obtained. When the cavity length is detuned away from such resonances, modulated continuous output is generated. The transition from mode-locked to modulated CW operation is explored experimentally for a Ce:LiCAF laser operating at 290 nm and pumped by a 78.75 MHz mode-locked frequency quadrupled Nd:YVO(4) laser. Both CW output and mode-locked output with pulse repetition rates up to 1.1 GHz were achieved. A rate equation model is developed to predict optimum cavity lengths for achieving CW output with minimized modulation.