The theory of orders and maximal orders over Dedekind domains or valuation-rings is an important ingredient in the study of arithmetical properties of algebras, in particular central simple algebras over fields. In [2], Larson introduced certain Hopf orders in a group algebra KG, where G is a finite group. The essential tool is a Zassenhaus valuation of G. Because of the multiplicative nature of that theory, those so-called Larson orders cannot be defined in other Hopf algebras without essential modification of the theory. In this paper we present the idea to replace the valuation filtration by a more general filtration, obtaining a bijective correspondence between the “Hopf filtrations” thus obtained and Hopf orders appearing as the degree zero part in such filtration. Just like in the group algebra case it is then possible to relate a Hopf order to an arithmetical object, i.e., a function ξ :H → R+ ∪ {∞}. These functions exhibit specific properties comparable to the ones expected for a valuation-like order function, i.e., so that −ξ should rightfully be called a “Hopf valuation.” We point out that −ξ can be expressed as a function defined on subspaces in H so that it may be thought of as a generalized place (pseudo-place) in the sense of [4]. In Section 2 we introduce the deformation of a Hopf (valuation) filtration and establish how it can be used to construct new Hopf orders. This explains in a general Hopf algebra framework how Larson-type orders come into being. We provide several examples, e.g., for Sweedler’s 4-dimensional Hopf algebra, Taft algebras, etc. in Section 4. In a forthcoming paper we apply the theory of Hopf orders to the theory of orders in H -module algebras.