We report an in situ heat-treatment technique for the preparation of near-fully-dense un-doped MgB2 bulks that also provides very strong in-field pinning. The high density was achieved without using high-pressure apparatus. The heat-treatment of compacted boron sealed in a Ta tube with Mg pellets employs a short high-temperature sintering at 1100 degrees C first, followed by a low-temperature annealing below 660 degrees C. A high density of 2.5 g cm(-3) (95% of the theoretical density) was achieved in the bulks treated by the two-step process. The in-field J(c) is nearly one order of magnitude higher than for the samples prepared by single-step sintering at high or low temperature. Microstructural analysis suggested a unique feature of well-connected small grains with a high level of disorder in the MgB2 samples created by the two-step process.