GaInAs/InP as well as GaAs/InP and InAs/InP quantum wells have been grown in the monolayer thickness range by LP-MOVPE. In a "growth window" at low growth rates (0.5-0.7 ML/s) and low AsH3 pressure (1 X 10(-3) Molar fraction) on exactly oriented (001) InP substrates the AsH3 interaction with the InP surface can be drastically reduced. Excellent QW luminescence corresponding to integer-number of quantum well thickness with no detectable interface effects at the lower interface could be observed. The 1 ML thick QWs of InAs/InP, GaInAs/InP and GaAs/InP show sharp luminescence peaks at 1.29, 1.305 and 1.327 eV. "Noninteger ML peaks" appear at higher growth rates and at substrate edges with a higher step density. The origin of these additional peaks are discussed.