We describe the investigation of methodologies for the creation of very high affinity human antibodies. The high affinity human antibody b4/12 was optimized for its affinity to the human envelope glycoprotein gp120 of human immunodeficiency virus type 1 (HIV-1). Five libraries of b4/12 were constructed by saturation mutagenesis of complementarity-determining regions (CDRs). Libraries of antibody Fab fragments were displayed on the surface of filamentous phage and selected in vitro for binding to immobilized gp120. Sequential and parallel optimization strategies of CDRs were examined. The sequential CDR walking strategy consistently yielded b4/12 variants of improved affinity in each of the four different optimization sequences examined. This resulted in a 96-fold improvement in affinity. Additivity effects in the antibody combining site were explored by combining independently optimized CDRs in the parallel optimization strategy. Six variants containing optimized CDRs were constructed. Improvement of affinity based on additivity effects proved to be unpredictable but did lead to a modest improvement in affinity. Indeed, only one of the six combinations demonstrated additivity. The highest affinity Fab prepared using this strategy was improved 420-fold in affinity. The affinity of this Fab was 15 pM as compared to 6.3 nM for b4/12. Examination of the kinetics of Fab binding to gp120 revealed that improvements in affinity were dominated by a slowing of the off-rate of the Fab. The methodology presented here provides a route for the improvement of the affinities of antibodies typical of tertiary immune responses into the picomolar range. Such improvements may have profound effects on the utility of antibodies as therapeutic and prophylactic agents.