New experiments in sensitive calorimeters displayed the characteristics of the excess power effect during seven different occasions. These measurements clearly show the anomalous increase in the cell temperature despite the steadily decreasing electrical input power during Pd/D2O + LiOD/Pt electrolysis. This strange behavior can be modeled by the use of an anomalous excess power term in the calorimetric equations. Two thermistors used in each calorimetric cell always show nearly identical temperature changes, thus errors due to temperature gradients within the cell are unlikely. The onset of the excess power apparently develops in a gradual manner. There were never any large, abrupt increases in the excess power. The addition of D2O with its sudden cooling of the cell generally dissipated the excess power effect. No clear triggering events for the excess power could be identified. Several possible chemical processes considered do not explain the excess power. Normal behavior was always observed for a similar experiment conducted as a control.