The best replacement for damp is dampen.

The best alternatives to damp are rated as following:
★★★★★  dampen
★★★★  condensation
★★★  moist
★★  mould
★★  water absorb
★★  humid
★  mildew
★  condensation difference
★  condensation mould
  leak
  dry soil
  damp cold
  slightly wet

Your alternative for damp is not listed? Suggest!
Speaking about damp, one probably shouldn't forget about cavity wall insulation.

Other search terms related to damp and their ratings are:
★★★★★ cavity wall insulation
★★ mould
★ cavity wall
You have in mind a companion for damp and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of damp in all years. Click on graph for more.
damp
dampen
condensation