  We present improved nucleon-nucleon potentials derived in chiral effective
field theory up to next-to-next-to-next-to-leading order. We argue that the
nonlocal momentum-space regulator employed in the two-nucleon potentials of
Refs. [E. Epelbaum, W. Gloeckle, U.-G. Mei{\ss}ner, Nucl. Phys. A747 (2005)
362], [D.R. Entem, R. Machleidt, Phys. Rev. C68 (2003) 041001] is not the most
efficient choice, in particular since it affects the long-range part of the
interaction. We are able to significantly reduce finite-cutoff artefacts by
using an appropriate regularization in coordinate space which maintains the
analytic structure of the amplitude. The new potentials do not require the
additional spectral function regularization employed in Ref. [E. Epelbaum, W.
Gloeckle, U.-G. Mei{\ss}ner, Nucl. Phys. A747 (2005) 362] to cut off the
short-range components of the two-pion exchange and make use of the low-energy
constants c_i and d_i determined from pion-nucleon scattering without any fine
tuning. We discuss in detail the construction of the new potentials and
convergence of the chiral expansion for two-nucleon observables. We also
introduce a new procedure for estimating the theoretical uncertainty from the
truncation of the chiral expansion that replaces previous reliance on cutoff
variation.
