Conrad was a member of the powerful Welf family, son of Count Heinrich of Altdorf. After an education at the cathedral school in Constance, he became provost of Constance Cathedral and in 934 was made Bishop of Constance. It is counted as one of his achievements that he avoided becoming enmeshed in the politics of the day and reserved his energies for his episcopal duties. He was nevertheless close to Emperor Otto I, whom he accompanied to Italy in 962. Conrad made three pilgrimages to Jerusalem as well as a number to Rome. He founded a number of churches on the episcopal estates and the hospital at Kreuzlingen, named after a portion of the True Cross which Conrad brought back from Jerusalem and presented to it.