we instead fit the drift rate as an independent parameter. Its initial values were stepped in a range from zero to $25^{\circ}/{\rm day}$. This range encompassed all plausible values for the flattening of the primaries and other parameters of the systems.

Since we found that the upper limits on eccentricity were low, in further modeling of the data from all apparitions together, we set the eccentricity equal to zero for simplicity and efficiency. This assumption had a negligible effect on the accuracy of other derived parameters of the models.

Across all observations, we found a unique solution for the system parameters except for an ambiguity in the quadratic drift in mean anomaly and the orbital period of 2001 SL9, see Tables \[tablePropKW4\] and \[tablePropSL9\]. We describe and discuss these parameters in Sections \[ParamsKW4\] and \[ParamsSL9\]. Plots of the RMS residuals (root mean square of observed magnitudes minus the values calculated from the model) vs $\Delta M_d$ are shown in Figs. \[RMS\_vs\_DMdKW4\] and \[RMS\_vs\_DMdSL9\]. In order to save computing time, the plots were constructed using spherical shapes of both components. However, neighborhoods of local minima were then revisited using elipsoidal shapes in order to improve the fit.

For 1999 KW4, the 