and it is natural to consider instead some type of quasiconformal mapping. One such class is [*quasisymmetric mappings*]{}, and a large body of recent literature is dedicated to quasisymmetric uniformization of metric spaces. We mention specifically papers by Semmes [@Sem:96b] and Bonk–Kleiner [@BonkKle:02] as important references.

Another approach is to use the so-called [*geometric definition*]{} of quasiconformal mappings, based on the notion of modulus of a curve family. In the recent paper [@Raj:16], the first-named author proves a version of the uniformization theorem for metric spaces homeomorphic to $\mathbb{R}^2$ with locally finite Hausdorff 2-measure. In the present paper, we call such spaces [*metric surfaces*]{}.

In [@Raj:16] a condition on metric surfaces called [*reciprocality*]{} (see Definition \[defi:reciprocality\] below) is introduced and shown to be necessary and sufficient for the existence of a quasiconformal parametrization by a domain in $\mathbb{R}^2$. We refer the reader to the introduction of [@Raj:16] for a detailed overview of the problem and additional references to the literature.

In this paper, we show that one part of the definition of reciprocality is satisfied by all metric surfaces and therefore is unnecessary. This result gives a positive answer to Question 17.5 from [@Raj:16].

We first recall the relevant definitions 