This paper examines “Extended Black” term structure models (EBTSM), which are multi-factor extensions of the one-factor Black model (Black, F., 1995. Interest rates as options. Journal of Finance 50, 1371–1376). EBTSM are not affected by the admissibility restrictions that plague canonical affine models. EBTSM encompass quadratic models, but unlike in quadratic models bond yields are sufficient statistics to infer the latent factors driving the short interest rate. EBTSM are amenable to econometric estimation despite the need to solve bond pricing equations through finite difference numerical methods. Estimation through the Iterated Extended Kalman filter reveals that a two-factor EBTSM fit well the observed cross section and time series of Japanese Government bond yields. A three-factor EBTSM is also proposed.