We characterize the positively charged exciton (X1+) in single InGaAs quantum dots using resonant laser spectroscopy. Three samples with different dopant species (Be or C as acceptors, Si as a donor) are compared. The p-doped samples exhibit larger inhomogeneous broadening (x3) and smaller absorption contrast (x10) than the n-doped sample. For X1+ in the Be-doped sample, a dot dependent non-linear Fano effect is observed, demonstrating coupling to degenerate continuum states. However, for the C-doped sample, the X1+ lineshape and saturation broadening follows isolated atomic transition behaviour. This C-doped device structure is useful for single hole spin initialization, manipulation, and measurement. (C) 2011 American Institute of Physics.