Short-wavelength GaInP/AlGaInP quantum-well (QW) laser diodes emitting in the 618-650 nm range at room temperature have been fabricated and characterized. Several variations in laser structures have been tested, including changes in QW composition, thickness, strain and number; changes in the barrier/waveguide composition and thickness; changes in cladding structure; use of multi-quantum-barriers and changes in the doping profile. The experiments showed that the threshold current characteristic temperature (T0) increases with the number of QWs and is higher for compressive strain. The use of graded-index (GRIN) waveguides and higher p-cladding doping induced both a reduction in threshold current density and an increase in T0, mostly at shorter wavelengths. Waveguide thickness optimization can be carried out, for both constant composition and GRIN waveguides, using the QW optical confinement as a first-approximation optimization criterion. Modified cladding structures reduced the vertical far-field full-width-at-half-maximum below 20° without significantly affecting the threshold current. Devices designed using some of the guidelines resulted from our study achieved, with different structures and under different operating conditions, performances like emitting more than 2W at 650 nm in continuous wave operation or lasing down to 618 nm at room temperature, which is among the shortest wavelengths from lasers grown by solid-source molecular-beam-epitaxy.