A renewed attempt is made to model anomalous cosmic ray He+ spectra observed during the solar minimum periods of 1977/1978, 1987, and 1997, from 1 to 66 AU in the heliosphere. This model improves on the one in our paper 3 in this series [Reinecke et al., 1996>, because it now contains the new 1997 observations, and because a physically justified input spectrum for anomalous species on the solar wind termination shock is used. This input spectrum is based on the work of Steenberg [1998> and Steenberg and Moraal [1999>. For simplicity, only anomalous He+ is considered. This is partially justified because the properties of other anomalous species, such as O+, are quite similar. This paper extends the work of paper 4 in the series [Reinecke et al., 2000>, in which similar fits to galactic He++ were done. It is shown that it remains impossible to find a single set of modulation parameters that fit the 1977, 1987, and 1997 anomalous and galactic spectra simultaneously. In addition, the new 1997 observations introduce further constraints that make it impossible to even find a single set of parameters for 1977 and 1997 with the current model, although these two periods are in the same so-called drift cycle. ¿ 2000 American Geophysical Union