  We solve the superspace Bianchi identities for ten-dimensional supersymmetric
Yang-Mills theory without imposing any kind of constraints apart from the
standard conventional one. In this way we obtain a set of algebraic conditions
on certain fields which in the on-shell theory are constructed as composite
ones out of the physical fields. These conditions must hence be satisfied by
any kind of theory in ten dimensions invariant under supersymmetry and some,
abelian or non-abelian, gauge symmetry. Deformations of the ordinary SYM theory
(as well as the fields) are identified as elements of a certain spinorial
cohomology, giving control over field redefinitions and the distinction between
physically relevant higher-order corrections and those removable by field
redefinitions. The conditions derived severely constrain theories involving
F^2-level terms plus higher-order corrections, as for instance those derived
from open strings as effective gauge theories on D-branes.
