  Recently the second and third author developed an iterative scheme for
obtaining rough solutions of the 3D incompressible Euler equations in H\"older
spaces (arXiv:1202.1751 and arXiv:1205.3626 (2012)). The motivation comes from
Onsager's conjecture. The construction involves a superposition of weakly
interacting perturbed Beltrami flows on infinitely many scales. An obstruction
to better regularity arises from the errors in the linear transport of a fast
periodic flow by a slow velocity field.
  In a recent paper P. Isett (arXiv:1211.4065) has improved upon our methods,
introducing some novel ideas on how to deal with this obstruction, thereby
reaching a better H\"older exponent - albeit below the one conjectured by
Onsager. In this paper we give a shorter proof of Isett's final result,
adhering more to the original scheme and introducing some new devices. More
precisely we show that for any positive $\epsilon$ there exist periodic
solutions of the 3D incompressible Euler equations which dissipate the total
kinetic energy and belong to the H\"older class $C^{\frac{1}{5}-\epsilon}$.
