We use asymptotic analysis and a near-identity normal form transformation f
rom water wave theory to derive a 1 + 1 unidirectional nonlinear wave equat
ion that combines the linear dispersion of the Korteweg-deVries (KdV) equat
ion with the nonlinear/nonlocal dispersion of the Camassa-Holtn (CH) equati
on. This equation is one order more accurate in asymptotic approximation be
yond KdV, yet it still preserves complete integrability via the inverse sca
ttering transform method. Its traveling wave solutions contain both the KdV
solitons and the CH peakons as limiting cases.