Charging circuitry is disclosed for receiving a magnetic charging field and using the received field to charge a battery in an Implantable Medical Device (IMD) without passive trickle charging, and even if the battery voltage (Vbat) is severely depleted. The charging circuitry includes a source capable of producing a constant charging current via a current mirror that receives a reference current for setting the charging current. Two reference current generators are provided: a first enabled when Vbat is severely depleted to produce a small non-adjustable reference current; and a second enabled once Vbat is recovered to produce a reference current that can be controlled to adjust the charging current. Because Vbat may be too low, the first generator is powered by a DC voltage produced from the magnetic charging field. A passively-generated undervoltage control signal is used to transition between use of the first and second generators.