Translation look aside buffer (TLB) hardware is provided in a central processor (CP) that receives the results of double-level address translations to eliminate the need for having shadow tables for the second-level in a virtual machine (VM) environment. Hardware is provided for indicating whether a requested address sent by the CP Instruction Execution (IE) unit for translation is a guest or host/native request, and for a guest request whether it is a real or virtual address. Intermediate translations for a double-level translation may or may not be inhibited from being loaded into the TLB. Guest entries may be purged from the TLB without disturbing any host entries. An accelerated preferred guest mode in the CP forces single-level translation hardware to translate each accelerated preferred guest request. A non-accelerated guest request may instead be translated by microcode. A limit check register is provided to check preferred guest addresses without causing performance degradation.