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Using the Calder\'on-Zygmund decomposition, we give a novel and simple proofthat $L^2$ bounded dyadic shifts admit a domination by positive sparse formswith linear growth in the complexity of the shift. Our estimate, coupled withHyt\"onen's dyadic representation theorem, upgrades to a positive sparsedomination of the class $\mathcal U$ of singular integrals satisfying theassumptions of the classical $T(1)$-theorem of David and Journ\'e, withlogarithmic-Dini type smoothness of the integral kernel. Furthermore, our proofextends rather easily to the $\mathbb R^n$-valued case, yielding as a corollarythe operator norm bound on the matrix weighted space $L^2(W; \mathbb R^n),$  \[  \left\|T\otimes \mathrm{Id}_{\mathbb R^n}\right\|_{L^2(W; \mathbbR^n)\rightarrow L^2(W; \mathbb R^n)} \lesssim [W]_{A_2}^{\frac32}  \] uniformly over $T\in \mathcal U$, which is the currently best knowndependence.

Uniform sparse domination of singular integrals via dyadic shifts