Work in ZF + AD + V = L(R). Given a nice countable set X of reals, it is natural to ask whether X is a mouse set: whether there is a mouse M such that X = R ∩ M, where R is the set of real numbers. Also,, how correct is X (how elementary is X in R, for example)? For example, the set of all OD reals is a mouse set (see [9]). In this talk, we consider more local versions of ordinal definability. At the projective level, R ∩ M_n is exactly the set of reals which are ∆^1_{n+2} in a countable ordinal, where M_n is the canonical proper class mouse with n Woodins. Also, M_{2n} is Σ^1_{2n+2}-correct but not Σ^1_{2n+3}-correct, and M_{2n+1} is also Σ^1_{2n+2}-correct but not Σ^1_{2n+3}-correct. Further, defining M_0=L and M_{−1} = L_{ω_1^{ck}}, the analogous results hold for these models, except that R ∩ L_{ω_1^{ck}} is the set of ∆^1_1 reals (in no parameters).) Moreover, writing <^{M_n} for the usual wellorder of M_n, <^{M_n} ↾ R^{M_n} is (∆^1_{n+2})^{M_n}-definable. Although M = L_{ω_1^{ck}} is not Σ^1_1-correct, it can define Σ^1_1 truth, via "anti-correctness", due to Spector-Gandy and Ville: – (Π^1_1)^V ↾ M is uniformly (Σ^1_1)^M , meaning that there is a recursive map f, with f(ϕ) = ψ_ϕ, sending Π^1_1 formulas ϕ to Σ^1_1 formulas ψ_ϕ, such that for all x ∈ R ∩ M, we have ϕ(x) ⇐⇒ M models ψ_ϕ(x). – Similarly, (Π^1_1)^M is uniformly (Σ^1_1)^V ↾ M . Higher up, (Σ^1_3)^V ↾ L is not definable over L, and in fact, there are ∆^1_3 reals which are not in L. But the anti-correctness for L_{ω_1^{ck}} has an analogue for M1 and Π^1_3. We will discuss various new results along these lines at levels of the Levy hierarchy through L(R).