The paper studies the existence of nontrivial real-valued, resp. rational-valued, irreducible \(p\)-Brauer characters of degree coprime to \(q\) for a finite group \(G\), where \(p\neq 2\) and \(q\) are primes. The author proves that, if \(G\) is both \(p\)-solvable and \(q\)-solvable, then such Brauer characters exist precisely when the normalizer \(N_G(Q)\) of a Sylow \(q\)-subgroup \(Q\) of \(G\) has even order. It was shown by \textit{G. Navarro} and the reviewer [in Math. Ann. 335, No. 3, 675-686 (2006; Zbl 1106.20006)] that \(G\) has nontrivial rational-valued irreducible \(p\)-Brauer characters if and only if \(|G|\) is even. The main result of the paper does not hold if \(p=2\), or if \(G\) fails to be \(p\)-solvable or \(q\)-solvable.