AIRS was launched on EOS Aqua on May 4, 2002, together with AMSU-A and HSB, to form a next generation polar orbiting infrared and microwave atmospheric sounding system. The primary products of AIRS/AMSU-A are twice daily global fields of atmospheric temperature-humidity profiles, ozone profiles, sea/land surface skin temperature, and cloud related parameters including OLR. The sounding goals of AIRS are to produce 1 km tropospheric layer mean temperatures with an rms error of 1K, and layer precipitable water with an rms error of 20 percent, in cases with up to 80 percent effective cloud cover. The basic theory used to analyze AIRS/AMSU/HSB data in the presence of clouds, called the at-launch algorithm, and a post-launch algorithm which differed only in the minor details from the at-launch algorithm, have been described previously. The post-launch algorithm, referred to as AIRS Version 4, has been used by the Goddard DAAC to analyze and distribute AIRS retrieval products. In this paper we show two candidates for the AIRS Version 5 algorithm which will be used by the Goddard DAAC starting late in 2006. The methodology used in each is otherwise identical, but one version uses only AIRS observations in the generation of cloud cleared radiances, while the other uses both AIRS and AMSU-A observations as done previously. Improvements made to the retrieval algorithm since Version 4 are described as well as results comparing retrieval accuracy and spatial coverage of each candidate for Version 5 with each other and with those obtained using Version 4.