Since Redington (1952) it has been recognized that classical immunization theory fails when shifts in the term structure are not parallel. Using partial durations and convexities to specify immunization bounds for non-parallel shifts in yield curves, Reitano (1991a,b) extended classical immunization theory to admit non-parallel yield curve shifts, demonstrating that these bounds can be effectively manipulated by adequate selection of the securities being used to immunize the portfolio. By exploiting properties of the multivariate Taylor series expansion of the fund surplus value function, this paper extends this analysis to include time values, permitting a connection to results on the time value-convexity tradeoff. Measures of partial duration, partial convexity and time value are used to investigate the generality of the duration puzzle identified by Bierwag et al.(1993) and Soto (2001).