D-term inflation in type I string theory

D-term inflation realized in heterotic string theory has two problems: the scale of the anomalous D-term is too large for accounting for COBE data and the coupling constant of the anomalous U(1) is too large for supergravity to be valid. We show that both of these problems can be easily solved in D-term inflation based on type I string theory or orientifolds of type IIB strings.