  This paper, together with a subsequent paper, questions the so-called 'LSND
anomaly': a 3.8 {\sigma} excess of anti-electronneutrino interactions over
standard backgrounds, observed by the LSND Collaboration in a beam dump
experiment with 800 MeV protons. That excess has been interpreted as evidence
for the anti-muonneutrino{\to} anti-electronneutrino oscillation in the
{\Delta}m2 range from 0.2 eV2 to 2 eV2. Such a {\Delta}m2 range is incompatible
with the widely accepted model of oscillations between three light neutrino
species and would require the existence of at least one light 'sterile'
neutrino. In this paper, new data on pion production by protons on nuclei are
presented, and four decades old data on pion production by neutrons on nuclei
are recalled, that together increase significantly the estimates of standard
backgrounds in the LSND experiment, and decrease the significance of the 'LSND
anomaly' from 3.8 {\sigma} to 2.9 {\sigma}. In a subsequent paper, in addition
the LSND Collaboration's data analysis will be questioned, rendering a further
reduction of the significance of the 'LSND anomaly'.
