The preparation and characterization of thick InP layers by Liquid Phase Epitaxy with admixture of Ce, Tb, Dy and Yb in the growth melt is reported. Measurement of temperature dependent Hall affect, C-V characteristics and low-temperature photoluminescence show the change of n -> p type conductivity and considerable improvement of structural and electro-optical parameters for all studied rare-earth elements. Mn was identified as dominant acceptor impurity in the case of Tb and Dy addition. In the case of Ce and Yb the dominant acceptor was identified as isoelectronic Ce or Yb on the In site subjected to a strong electron-lattice interaction. The reported high quality thick p-type InP layers could well be used for the preparation of radiation detector structures.