Transport measurements were made to study the superconducting transition of four 6 mm long niobium nanowires with different cross-sectional dimensions. A low-temperature residual resistance measured with an excitation current of 5 nA is found in the thinnest wire down to 50 mK or 7.7% of T-c of Nb. The functional form of the residual resistance is consistent with quantum phase slip (QPS) processes. Resistance measured at high bias excitation current switches among many discrete values that are well below the normal state resistance. These discrete resistance values as a function of temperature fall into several parallel curves all showing QPS-like decay in the low temperature limit similar to that found at low current. The coexistence of QPS-like resistance tails and resistance jumps found in the same wire unifies results from previous experiments where these two distinct sets of evidence for QPS are exclusive of each other.