Steepness effects of pump pulse temporal profile on supercontinuum spectrum in an all-solid, normally dispersive photonic crystal fiber are investigated numerically. Utilizing a multi-shot supercontinuum spectra generated with a statistical nonlinear Schrödinger equation model and computed spectral correlation maps, we discuss both the timescale and the spectral bandwidth of parametric interaction between self-phase modulation and optical wave-breaking components in the formation of the spectrum. Gaussian and hyperbolic secant pump pulse profiles, modelled with analytical formulas, are used to show the role of the wings of temporal pulse profile in the flatness of the developing supercontinuum from the perspective of spectral correlation. Degree of coherence of the numerical spectra is also analyzed and it is shown how steepened pump pulse slope preserves pump laser shot noise in otherwise coherent, normal dispersion supercontinuum generation. All-normal dispersion supercontinuum spectrum was also recorded experimentally in a photonic crystal fiber in the 1350–1750 nm range of wavelengths (E-U telecommunication bands), under 1550 nm pumping with 180 fs pulses and moderate in-coupled energy of 1 nJ, reproducing the bandwidth and general features of one of the numerical cases.