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Assuming perfect detection efficiency, we present an (indeterministic) modelfor an EPR-Bohm experiment which reproduces the singlet correlations, withoutcontradicting Bell's original locality condition. In this model we allow theprobability distribution $\rho_{\lambda}$ of the state $\lambda$ at the sourceto depend parametrically on the orientation $\xi$ of one of the measuringdevices: $\rho_{\lambda}(\lambda,\xi)$. In a Bell experiment, no-signalingbetween the source and each one of the devices would seem clearly sufficient torule such an influence; however, not even schemes where the choice ofobservables takes place during the on-flight time of the particles can prevent,in some situations, a model of this type from violating the local bounds. Inparticular, a random shift $\rho_{\lambda}(\lambda,\xi_1) \rightarrow\rho_{\lambda}(\lambda,\xi_2) \rightarrow...\rightarrow\rho_{\lambda}(\lambda,\xi_n)$ allows the model to perform a "subensembleselection" for each of the terms involved in the inequality (analogous to whatgoes on with the efficiency loophole), whenever some correlation of those$\rho_{\lambda}$-shifts with the sequence of measurement choices is allowed.That correlation does not necessarily imply signaling during the photonon-flight time.

Communication loophole in a Bell-EPR-Bohm experiment: standard no-signaling may not always be enough to exclude local realism