We study the contribution of a truncated Balitskii-Fadin-Kuraev-Lipatov Pom
eron series to the hadronic processes showing that a reliable description i
s obtained using two orders in perturbation theory. The pp(p (p) over bar)
total cross sections are described with good agreement, consistent with the
unitarity bound. We also calculate the elastic-scattering amplitude at non
zero momentum transfer t, introducing two distinct Ansatze for the proton i
mpact factor. As a by product the elastic differential cross section is obt
ained at the small t approximation and compared with the data, describing w
ith good agreement this observable for both low- and high-energy values.