In this letter, we report the design and operation of multiple-quantum-well distributed Bragg reflectors (MQW DBR) lasers with monolithically integrated external-cavity electroabsorption (EA) modulators without modification of the active region fabricated using only a single growth step, Devices were fabricated with operating wavelengths of 1.06, 1.07, and 1.08 mu m, which are red-shifted from the material gain peak wavelength (lambda=1.05 mu m) by 100, 200, and 300 Angstrom, respectively. The lambda=1.06-mu m device has a continuous-wave (CW) threshold current of 16 mA and a slope efficiency of 0.09 W/A from the modulator facet, while the lambda=1.08 mu m device has a CW threshold current of 33 mA and a slope efficiency of 0.40 W/A from the modulator facet, The lambda=1.06-, 1.07-, and 1.08-mu m device exhibits an extinction ratio of greater than or equal to 120 dB at a modulator bias of 1.0, 1.4, and 2 V, respectively.