Previous experiments showed that eight electrolysis gas samples collected during episodes of excess power production in two identical cells contained measurable amounts of 4He while six control samples gave no evidence for helium. However, the detection limit for helium could not be defined clearly. This study of helium diffusion into the Pyrex glass sample flasks establishes a minimum helium detection limit of 3 × 1013 atom/500 ml (3 ppb) for these experiments. New D2O and H2O control experiments involving helium measurements of electrolysis gas samples collected in metal flasks support this conclusion. This places the 4He production rate at 1011 to 1012 atom/s per watt of excess power, which is the correct magnitude for typical fusion reactions that yield helium as a product. Simultaneous evidence for excess power, helium production, and anomalous radiation was present in these experiments. Completely new experiments with more precise helium measurements are reported that again show simultaneous evidence for excess power, helium production, and anomalous radiation.