Hessman was a Barrayaran admiral in charge of procurement for the Barrayaran Imperial Service. He was the political ally of Count Vordrozda, and conspired with him to kill Ivan Vorpatril and convict Miles Vorkosigan of treason for violating Vorloupulous's Law.
When reports from an agent of Chief of Imperial Security Simon Illyan arrived on Barrayar indicating Miles Vorkosigan was raising a private army, Hessman and Vordrozda saw an opportunity to destroy Prime Minister Aral Vorkosigan's Centrist coalition. Hessman arranged for the sabotage of the Necklin rods of the fast courier carrying the treason summons, while Vordrozda used his influence with Emperor Gregor Vorbarra to have Illyan imprisoned.
Hessman arranged for cadet Ivan Vorpatril to be aboard the doomed courier, but Vorpatril missed his rendezvous and was not aboard when the courier was lost during a wormhole jump. Vorpatril eventually reached Vorkosigan, who returned to Barrayar to face the treason charge. Hessman was giving testimony as a witness in the Council when the two Vor lords arrived.
Miles Vorkosigan confronted Hessman about the courier sabotage, and Hessman fingered his partner in crime Vordrozda. The furious Vordrozda drew a needler in the Emperor's presence, and was subdued by his fellow counts. Both conspirators were then arrested and removed from the Council chambers.