We report on p-channel metal-insulator-semiconductor heterostructure field-effect transistors (MISHFET) based on p-GaN/uid-GaN/Al0.29Ga0.71N single heterostructures on sapphire substrates, grown by metalorganic vapor phase epitaxy (MOVPE). The impact of p-GaN layer removal and channel layer thickness adjustment by dry-etching on the characteristics of the MISHFET are investigated. Depending on the remaining GaN thickness (tGaN), the fabricated MISHFET show either depletion-mode (d-mode) operation with a threshold voltage Vth of 3.8 V and an on-current |ID,on| of 9.5 mA/mm (tGaN = 21 nm) or enhancement-mode (e-mode) operation with Vth of -2.3 V and |ID,on| of 1.5 mA/mm (tGaN = 12 nm). Independent of the etching depth, all devices exhibit a very low off-state drain current |ID,off| 10-8 mA/mm and a steep subthreshold swing (SS) between 80 and 89 mV/dec. Similar to n-channel devices, a Vth instability caused by charge trapping at the dielectric/semiconductor interface is found, emphasizing that careful interface engineering is required for good device performance.