Divertor detachment may be essential to reduce heat loads to magnetic fusion tokamak reactor divertor surfaces. Yet in experiments it is difficult to control the extent of the detached, low pressure, plasma region. At maximum extent the front edge of the detached region reaches the X-point and can lead to degradation of core plasma properties. We define the 'detachment window' in a given position control variable C (for example, the upstream plasma density) as the range in C within which the front location can be stably held at any position from the target to the X-point; increased detachment window corresponds to better control. We extend a 1D analytic model [1] to determine the detachment window for the following control variables: the upstream plasma density, the impurity concentration and the power entering the scrape-off layer (SOL). We find that variations in magnetic configuration can have strong effects; increasing the ratio of the total magnetic field at the X-point to that at the target, , (total flux expansion, as in the super-x divertor configuration) strongly increases the detachment window for all control variables studied, thus strongly improving detachment front control and the capability of the divertor plasma to passively accommodate transients while still staying detached. Increasing flux tube length and thus volume in the divertor, through poloidal flux expansion (as in the snowflake or x-divertor configurations) or length of the divertor, also increases the detachment window, but less than the total flux expansion does. The sensitivity of the detachment front location, zh, to each control variable, C, defined as , depends on the magnetic configuration. The size of the radiating volume and the total divertor radiation increase and , respectively, but not by increasing divertor poloidal flux expansion or field line length. We believe this model is applicable more generally to any thermal fronts in flux tubes with varying magnetic field, and similar sources and sinks, such as detachment fronts in stellarator divertors and solar prominences in coronal loops.