History of the Byzantine Empire by Enno Franzius
It's hard to find information about this guy. It appears that he was a professor at Columbia University in NY and a prolific writer on various topics of history. However, most of his works seem to be out of print, and I suspect why which I'll get to in a minute.
This history starts at the Late Roman period because this allows him to lay out the background of the later Roman state centered on Byzantion. It ends with the final conquest of New Rome at the hands of the Osmanli hordes many centuries later.
It's written in an interesting style, almost like a novel at times in its narrative, including strange anecdotes and poetic styles. It also uses names that have fallen out of common use, calling early Russian raiders 'Northmen' and calling the troublesome steppe nomads 'Patzinaks'. The stylistic elements combine to make it a pretty strange but interesting read compared with the dry styles of current historiography.
He is not always PC in his descriptions and makes an attempt to classify all the peoples associated with this long period by race. He includes to this end descriptions by chroniclers and observers of the times. This is something you'd never see in a contemporary book and it definitely is this sort of thing that makes me feel it is unlikely to re-enter print given the biases of modern publishers.
In addition to covering the major historical developments, he also does a good job with the political-economic organization of the empire at various times. Examples include development of the Thematic system at the imperial apex, or the central-bureaucratic meddling that ruined things later on. He also describes the factional struggles of the various families of the time in some detail.
Other interesting things are found here too. For example, occasional descriptions of particular rulers, both physically and with respect to their character. Or, in-depth discussions of the cultural currents of the time, such as Justinian's building program, or the Iconoclasm controversy, or the theological struggles that split the empire at times. These cultural observations I found surprisingly rich.
I could go on, but I won't. It's a book well worth reading should you be able to find a copy. For a book that covers ground many others have trod before, it actually does a good job of making it seem fresh.