  By an odd structure we mean an algebraic structure in the category of graded
vector spaces whose structure operations have odd degrees. Particularly
important are odd modular operads which appear as Feynman transforms of modular
operads and, as such, describe some structures of string field theory.
  We will explain how odd structures are affected by the choice of the monoidal
structure of the underlying category. We will then present two `natural' and
`canonical' constructions of an odd modular endomorphism operad leading to
different results, only one being correct. This contradicts the generally
accepted belief that the systematic use of the Koszul sign convention leads to
correct signs.
