Early Tuesday evening, about 20,000 customers were still out, about half as many as earlier in the day, and a fraction of the 400,000 reported at the height of the storm.
NStar was reporting about 16,000 outages early Tuesday evening, with Duxbury, Marshfield and Plymouth among the hardest hit communities. The utility says it could be Thursday night before some get the power back.
National Grid was reporting about 3,300 outages, most in Plymouth.
The companies say their crews have been hampered by severe damage to lines and equipment, access challenges posed by snowdrifts and unplowed and narrower-than-normal streets.