Pilot of light twin experiences a rough running engine at 5000 feet; over water; on an IFR flight plan. Reporter informs ATC of his plan to divert and proceeds direct; without clearance or declaring an emergency.

Narrative

While flying over the ocean at 5000' MSL; my left engine became rough. I informed Center that I had a rough left engine and was diverting to ZZZ. I turned direct to ZZZ. ATC immediately handed me off to Approach Control. On initial call-up; I informed Approach that I was proceeding direct ZZZ. Approach informed me that I was not authorized to proceed direct ZZZ and gave me a heading to fly. I turned to the heading and informed Approach that I had a rough left engine and would like to proceed direct to ZZZ. Approach told me to standby and then handed me off to another Approach Controller who cleared me direct ZZZ. This Controller asked if I was declaring an emergency. I replied no; that my left engine was rough and that I wanted to check it on the ground. At no time did I feel the flight was in any danger or jeopardy. As a precaution; I had decided to land and check the situation on the ground. I associate the word emergency with a dire situation where flight safety is clearly in danger. However; in hindsight; and after reviewing the AIM; it is clear that if I wanted to deviate for ANY reason; precaution or otherwise; I should have declared an emergency. The AIM states that an emergency can either be a 'distress' or 'urgency' condition. An urgency condition is defined as: 'A condition of being concerned about safety and of requiring timely but not immediate assistance...' That is clearly the way I was handling this situation and so I should have declared an emergency. I believe that many; if not most pilots; only think of emergency as a 'distress' condition: 'A condition of being threatened by serious and/or imminent danger and of requiring immediate assistance'. It is important to understand that the FAA has provided a clear definition of emergency and that it may not exactly mirror our own definition of emergency. It is a tool for both pilot and controller for handling an anomaly. Probably most importantly; it provides the means for preventing an 'urgency' from becoming a 'distress'.