Is it possible to offer Communion to non-Catholics?

By direction of the U.S. Conference of Catholic Bishops, there appears a statement of guidelines for the reception of Communion in every missalette.

In the case of Christians who are not Catholics, the guide-lines say:

We welcome to this celebration of the Eucharist those Christians who are not fully united with us. It is a consequence of the sad divisions in Christianity that we cannot extend to them a general invitation to receive Communion. Catholics believe that the Eucharist is an action of the celebrating community signifying a oneness of faith, life and worship of the community. Reception of the Eucharist by Christians not fully united with us would imply a oneness which does not yet exist, and for which we all must pray.

In the case of those who are not Christians, the guidelines say:

We also welcome to this celebration those who do not share our faith in Jesus. While we cannot extend to them an invitation to receive Communion, we do invite them to be united with us in prayer. In other words, according to the guidelines established by the Holy See, those who are not Catholic are not to be invited to Communion. There are some circumstances and situations when the Eucharist may be given to Christians who share our belief in the real presence of Jesus in the Eucharist. In the case of Eastern (Orthodox) Catholics not in union with Rome, they must spontaneously ask for the sacrament and be properly disposed.

Non-Catholics may be given the Eucharist if they are in danger of death or if there is some other serious need, in the judgment of the local bishop or episcopal conference. But in such cases the Christian non-Catholics must be unable to go to a minister of their own community and they must spontaneously ask for the sacrament. They must manifest Catholic faith in the sacrament and be properly disposed.