Subtyping is a common tool in the design of type systems that finds itsroots in the eta-expansion of arrow types and the notion of typecontainment obtained by closing System Fby eta-expansion. Althoughstrongly related, subtyping and type containment still significantlydiffer from one another when put into practice. We introduce coercionconstraints to relate and generalize subtyping and type containment aswell as all variants of F-bounded quantification and instance-boundedquantification used for first-order type inference in the presence ofsecond-order types. We obtain a type system with a clearer separationbetween computational and erasable parts of terms.