The invention relates to a process for producing rigid polyurethane and polyisocyanurate foams by reacting polyisocyanates a) with compounds having at least two hydrogen atoms which are reactive toward isocyanate groups b) in the presence of blowing agents c), wherein prepolymers which comprise isocyanate groups and have an NCO content in the range from 25 to 31% by weight, based on the weight of the prepolymer, and are prepared by reacting ai) mixtures of monomeric and polymeric diphenylmethane diisocyanate with at least one compound having more than one hydrogen atom which is reactive toward isocyanate groups aii) are used as polyisocyanates a) and the compounds having at least two hydrogen atoms which are reactive toward isocyanate groups b) comprise at least one polyester alcohol bi) which comprises at least one starting component which is hydrophobic.