One-component reaction system for producing rigid polyurethane foams, comprising the following constituents: A) an organic polyisocyanate component which is partly in the form of a prepolymer (referred to as "semi-prepolymer" hereinbelow), wherein the organic polyisocyanate component A) is further characterized in that the content of free isocyanates not reacted with polyol measured as defined in the description is > 1% by weight to < 25% by weight based on the total weight of the component A) and in that the NCO content is > 7.5% by weight to 13.0% by weight, in particular > 8.0 to < 13.0% by weight, based on the total weight of the component A), B) optionally an isocyanate-reactive component whose isocyanate-reactive functional groups are exclusively those having at least one Zerewitinoff-active hydrogen atom, C) at least one foam stabilizer, D) at least one catalyst suitable for catalyzing the reaction of the semi-prepolymer with atmospheric humidity, E) at least one physical blowing agent having a boiling point of less than 0°C and optionally co-blowing agents and F) optionally assistant and additive substances, characterized in that the semi-prepolymer is formed by reaction of A.1) an organic polyisocyanate component A.1) consisting to an extent of at least 80% by weight of the monomeric diphenylmethane diisocyanates 2,4'-MDI, 2,2'-MDI and/or 4,4'-MDI and A.2) a polyol component A.2) having a functionality F n (based on the Zerewitinoff-active hydrogen atoms in the polyol component) of ≥ 2.0 to ≤ 3.0 and an OH number of 28 to 350 mg KOH/g, and wherein the proportion of the component B) is 0.00% by weight to 0.45% by weight based on the total weight of the components A) to F). A) an organic polyisocyanate component which is partly in the form of a prepolymer (referred to as "semi-prepolymer" hereinbelow), wherein the organic polyisocyanate component A) is further characterized in that the content of free isocyanates not reacted with polyol measured as defined in the description is > 1% by weight to < 25% by weight based on the total weight of the component A) and in that the NCO content is > 7.5% by weight to 13.0% by weight, in particular > 8.0 to < 13.0% by weight, based on the total weight of the component A), wherein the organic polyisocyanate component A) is further characterized in that the content of free isocyanates not reacted with polyol measured as defined in the description is > 1% by weight to < 25% by weight based on the total weight of the component A) and in that the NCO content is > 7.5% by weight to 13.0% by weight, in particular > 8.0 to < 13.0% by weight, based on the total weight of the component A), B) optionally an isocyanate-reactive component whose isocyanate-reactive functional groups are exclusively those having at least one Zerewitinoff-active hydrogen atom, C) at least one foam stabilizer, D) at least one catalyst suitable for catalyzing the reaction of the semi-prepolymer with atmospheric humidity, E) at least one physical blowing agent having a boiling point of less than 0°C and optionally co-blowing agents and F) optionally assistant and additive substances, A.1) an organic polyisocyanate component A.1) consisting to an extent of at least 80% by weight of the monomeric diphenylmethane diisocyanates 2,4'-MDI, 2,2'-MDI and/or 4,4'-MDI and A.2) a polyol component A.2) having a functionality F n (based on the Zerewitinoff-active hydrogen atoms in the polyol component) of ≥ 2.0 to ≤ 3.0 and an OH number of 28 to 350 mg KOH/g, and wherein the proportion of the component B) is 0.00% by weight to 0.45% by weight based on the total weight of the components A) to F).