Introduction. Links between operators and function theory are often fruitful in both directions. For example, in operator theory one tends to build models for various classes of Hilbert space operators, expressing them (up to some equivalence) as certain simple actions defined on suitable function spaces. Working in the opposite direction, one can view function-theoretic phenomena as statements about the related linear operators. Sometimes the interpretation of operations on functions via different functional models allows one to view them “at a more convenient angle”. The last section is intended to exemplify this approach and despite its simplicity, the underlying idea seems worth further studying. We begin with outlining the Hardy space model for a quite large class of subnormal operators S. Among various functional models preferred are those satisfying as much as possible of the following three postulates. Namely, they should be: 1 determined up to unitary equivalence, 2 acting by a simple formula, 3 defined on a space consisting of concrete functions (rather than, say, of distributions). All these three requirements are met by the model, introduced (under quite restrictive assumptions on the geometry of the spectrum σ(S) of S) by Abrahamse and Douglas [AD1], [AD2]. The first substantial relaxation of these geometric assumptions (still in the case of finitely connected σ(S)) was presented in [R1], but the serious difficulty in extending the model to (any) infinitely connected σ(S) was overcome in [R2] after the employment of new tools: W. Mlak’s absolute continuity result [M] and M. Hasumi’s and C. Neville’s extension of the Beurling–Lax theorem [H]. In the present paper we use the results of [S] to simplify the earlier construction [R2]. These results eliminate the need for certain additional assumptions and provide a better explanation of the role of other requirements.