backgrounds readings on gibbon (mostly late antiquity)

Here are some books I find helpful as we read the final chapters of Edward Gibbon's  The Decline And Fall  In The West, Volume 1.

• Barbarians and Romans: The Birth Struggle of Europe, A.D. 400-700
  by Justine Davis Randers-Pehrson
• From Roman Provinces to Medieval Kingdoms (Rewriting Histories)
  by Thomas Noble
• and this old standby, though a bit of a time stretch:
  Mohammed and Charlemagne
  by Henri Pirenne