A process for preparing a vinyl acetate-ethylene copolymer by means of free-radically initiated emulsion polymerization of vinyl acetate and ethylene and, optionally, further comonomers, performed in the presence of at least one protective colloid and at least one nonionic, ethoxylated emulsifier with an alkyl radical or at least one ethylene oxide-propylene oxide copolymer, and in the absence of chain transfer agent, and, before the initiation of the polymerization, 10% to 70% by weight of the vinyl acetate monomer and 40% to 100% by weight of the ethylene monomer are included in the initial charge, up to 100% by weight of the protective colloid fraction is included in the initial charge, at least 25% by weight of the emulsifier fraction is included in the initial charge, and the remaining fractions of monomers, protective colloid and emulsifier are metered in during the polymerization. A defined criterion of process COP is met.