We show that in O'Raifeartaigh models of spontaneous supersymmetry breaking,
R-symmetries can be broken by non-zero values of fields at tree level, rather
than by vacuum expectation values of pseudomoduli at loop level. As a
complement of the recent result by Shih, we show that there must be a field in
the theory with R-charge different from zero and two in order for R-symmetry
breaking to occur, no matter whether the breaking happens at tree or loop
level. We review the example by CDFM, and construct two types of tree level
R-symmetry breaking models with a wide range of parameters and free of runaway
problem. And the R-symmetry is broken everywhere on the pseudomoduli space in
these models. This provides a rich set of candidates for SUSY model building
and phenomenology.Comment: 8 pages; v2: major revision to section 6; v3: minor revision and
typos; v4: typos, published version; v5: fix Latex syntax error, published
versio