Sticking with the existing fleet for the 1954 season, Cunningham prepared to introduce a new lightweight vehicle, designated C-6R, the following year. The new car was to answer the lessons learned in past campaigns: to begin with, it would be smaller, much lighter, and incorporate right-hand drive.

That it was the first Cunningham racer built according to a full set of engineering drawings was reflected in its efficient packaging and elegant design. But the car also bore one glaring compromise, its use of a Mayer-Drake prepared Offenhauser four-cylinder engine rather than the Ferrari 375MM V-12 originally intended. The Offy was run first with Hilborn injection, then with Weber side-drafts which, with other changes, boosted output by 40HP to 260 at 6,000 rpm.

The chassis featured two triangular units extending from the front crossmember, reaching up to the cowl, then descending to meet the rear of the main frame. Front suspension consisted of unequal length A-arms and coil springs, and a Norden steering gear unit. The rear end once again used a De Dion layout incorporating inboard coil springs and brakes. Both tubular and Houdaille vane-type shock absorbers were used at all four corners.

Briggs and John Gordon Bennett first drove the unpainted car at Sebring in March 1955, dropping out when the flywheel disintegrated on the fifty-fourth lap.

The C-6R then appeared at Le Mans in June sporting a headrest/tailfin in the fashion of the D-Type Jaguars, and a smaller grille opening to aid the car's aerodynamics. Cunningham and Sherwood Johnston drove the car to speeds of up to 141.32 mph, but were forced to go progressively more slowly until all but top gear in the transmission gave up. The extra load was too much for the Offy, which already had inherent overheating problems caused by the conversion from alcohol to gasoline; the engine eventually ate one of its pistons, and the car retired after eighteen hours in 13th place.

Certainly an even greater disappointment was that, as a consequence of witnessing the massive accident that took so many lives at Le Mans that weekend, the immensely talented Phil Walters decided on the spot that he was through with racing. Said Briggs years later, "I can't say that I blame him."

Briggs drove the car again at the Road America season-opener where the plucky Offy finally expired for good. The car sat dormant until 1957, when Alfred Momo installed a 3.8-litre Jaguar engine and transmission. Cunningham entered the car at Sebring and cracked a cylinder wall during practice. It later ran in a couple of SCCA events before being permanently retired, and is now in the Collier collection in Florida.