In this paper, a new concept of level-dependent Sugeno integral is introduced, and it is used to represent comonotone maxitive aggregation functions acting on a complete scale K. The relationship between the level-dependent Sugeno integral and some other types of fuzzy integrals is shown, and properties of the level-dependent Sugeno integral are discussed. Several examples show that the level-dependent Sugeno integral can have different aggregation attitudes for low input values than for high input values, and thus, overcome problems that arise while using the Sugeno integral.