We have studied the characteristics of 1.65-mum InAs self-organized quantum-dash lasers grown on InP (001) substrates, wherein special techniques of p-doping of quantum dashes and tunnel injection are incorporated for the first time. We measured a very large T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> (196 K) in p-doped quantum-dash lasers, accompanied by an increase in threshold current density (J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sub> ~1600 A/cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2 </sup> ), compared to the undoped quantum-dash lasers (T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> =76 K and J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sub> ~950 A/cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ). The p-doped lasers exhibit a maximum 3-dB bandwidth of 8 GHz, chirp ~1.0 Aring, and alpha-parameter ~1.0 (measured at subthreshold bias conditions) at a temperature of 278 K. Similar undoped quantum-dash lasers exhibit a 3-dB bandwidth of 6 GHz. A self-consistent model, that includes Auger recombination in quantum dashes, is developed to calculate the threshold current at various temperatures. A comparison of the calculated threshold current and T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> with measured values reveals that Auger recombination in quantum dashes plays a major role in determining the values of threshold current and T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> in both undoped and p-doped quantum-dash lasers. While p-doping increases the gain and differential gain, the presence of wetting layer states, the relatively large inhomogeneous broadening of quantum dashes, and the substantially increased Auger recombination upon p-doping severely limit the potential benefits. Superior characteristics, including large modulation bandwidth (f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3 dB</sub> ~12 GHz), near-zero alpha-parameter, and very low chirp (~0.3 Aring), are achieved when the technique of tunnel injection is also utilized