Saturation of the spontaneous emission intensity from stripe-geometry double-heterostructure junction lasers has been observed for currents from threshold up to three times threshold. The present observation of saturated luminescence depends upon the spatial uniformity of the saturated gain obtained in a laser with a thin active region (sim0.2-0.3 mum) and weak optical confinement. In lasers with thicker active regions (sim1 mum) and stronger optical confinement, the spontaneous emission does not saturate at threshold but continues to increase with current at a reduced rate. The increasing emission is shown to originate in spatial regions where the field intensity is low and consequently the gain is not saturated. At pumping levels high above threshold, the nonuniform saturation of the gain (transverse spatial hole burning) leads to increased gain and finally oscillation for other transverse modes.