We explore some of the controls on the evolution of a slow effusive eruption imposed by processes in a shallow magma reservoir. We envisage that the emplacement of basaltic magma into a shallow, evolved crustal reservoir generates sufficient overpressure to trigger the slow effusive eruption of the overlying layer of evolved magma. The subsequent evolution of the system then depends on a number of factors including (1) the volatile contents of the two magmas; (2) the rate of any continuing influx of basalt; (3) the cooling/heating rates of the two layers of magma; and (4) the eruption rate of the silicic magma, where we assume that the crystals and bubbles remain in the layer in which they formed. Any exsolved volatiles in the magma increase the compressibility of the magma. In a waning system, this tends to increase the volume of material, which needs to be erupted to relieve a given overpressure by an amount of order 10--100, and hence increases the duration of the eruption. Typical calculations suggest that eruptions from magma chambers of size 1--10 km3 may persist for times of order 1--10 years if the main body of silicic magma is saturated in volatiles. In addition, cooling of the basalt leads to formation of dense crystals, which lowers the pressure. However, if the magma becomes saturated, exsolution of volatile gases occurs, tending to increase the pressure. Again, in a waning system, this tends to extend the eruption duration and increase the mass erupted from the chamber. For chamber volumes of 1--10 km3, cooling rates of 10-6 K/s can increase the eruption volume by a factor of order 10. Rapid cooling may also lead to an initial increase in the eruption rate, while the chamber pressure is controlled by the rate of production of new bubbles. If there is an influx of basalt to the chamber which is maintained during the eruption, then the evolution of the eruption is primarily dependent on this input rate, although the cooling of the basalt may increase the eruption rate to values in excess of this input rate, especially at an early stage in the eruption. The complex and nonlinear evolution of the eruption rate predicted by our simple model illustrates the sensitivity of the eruption rate to the magma volatile content and magma cooling rates. Such understanding is key in developing quantitative models for hazard assessments of slow effusive eruptions.