The Reichsluftfahrtministerium (RLM, or Reich Aviation Ministry) first learned of the American B-29 Superfortress heavy bomber in late 1942. Serious concerns as to B-29 capability developed in early 1944, when YB-29 "Hobo Queen" made a well-publicised appearance at RAF Bovingdon, which had been cryptically hinted-at in an American-published Sternenbanner German language propaganda leaflet from Leap Year Day in 1944, meant to be circulated within the Reich.

The performance estimates of this aircraft were a cause for great unease in the Luftwaffe. The B-29 had a maximum speed of around 560 km/h (348 mph), and would attack in a cruise at about 360 km/h (224 mph) at 8,000-10,000m (26,247-32,810 ft), an altitude where no current Luftwaffe aircraft was effective, and for which the only effective Wehrmacht anti-aircraft gun was the rarely-deployed 12.8 cm FlaK 40, which could effectively fire to an altitude of 14,800 metres (48,600 ft).

To counter the B-29, the Luftwaffe would need new day fighters and bomber destroyers with greatly enhanced performance at extreme altitude. The fighter chosen was the Focke-Wulf Ta 152H. This was based on the Fw 190D with longer wings and the new high-altitude "E" model of the Junkers Jumo 213 engine. An alternative was the Messerschmitt Me 155B, a long-winged development of the Bf 109 which had already undergone several stages of design and would ultimately be built in prototype form by Blohm & Voss. The centre-line thrust twin Dornier Do 335, powered with two of the competing Daimler-Benz DB 603 engines also offered a service ceiling of some 11,400 m (37,500 ft), but the promising Dornier heavy fighter and Zerstörer was still under development solely with prototype airframes flying, and the first production examples expected to enter operational service late in 1944.

For the bomber destroyer and night fighter roles, the all-wood Focke-Wulf Ta 154 and metal-structured Heinkel He 219 had the performance needed to catch the bomber; however, both designs only gained that performance by mounting low aspect ratio wings which were inadequate for flight at high altitude and resultingly produced too high a wing loading. The Junkers Ju 88 had already been modified for high-altitude use as the S and T models, but these did not have the performance needed. Similar high-altitude modifications to the Ju 188, with its complex stepless cockpit glazing comprising some three dozen framed window panels in all, were being looked at as the projected Ju 188J, K and L models, which included a simplified "stepless" pressurized cockpit that fully enclosed the entire nose using fewer glazed panels in comparison to the Ju 188's glazing design, and wing and elevator deicing equipment for extended flights at very high altitude. These were selected for development, and renamed Ju 388.

Sources:
Gunston, Bill - The Encyclodepia of the Worlds Combat aircraft, 1976, Chartwell Books, Inc., New York
Brown, Eric, Captain - Wings of the Luftwaffe, 1979, Airlife Publishing Ltd., Shrewsbury
Gunston, Bill & Wood, Tony - Hitler's Luftwaffe, 1977, Salamander Books Ltd., London
Donald, David - The Complete Encyclopedia Of World Aircraft, 1997, Brown Packaging Books Ltd., London
Wikipedia - Junkers Ju 388