Issac II deals with Asen and Peter with a bit more tact and the second Bulgarian Empire never forms. What would be the effects on the 4th crusade and the years following it? What would a rump state in the region of Bulgaria look like?
Well it might be easier to avoid the rebellion from breaking out. The event was triggered by the special levy imposed by Isaakios II in order to cover the expenses of the wedding ceremony for his marriage to the daughter of Bela III of Hungary. If he had decided to economise a bit on that front, he could perhaps gain some time. This however would just be a temporary solution, for the real trouble was the maladministration of the Bulgarian provinces in the last years of Komneni rule and a feeling that the empire was vulnerable.
So Isaakios would have to tackle these issues. As far as the second of these was concerned (the perception of weakness), the repulsion of the Normans was a good start, while the closer ties with Hungary after the marriage could create the more restless Bulgarian elements the impression that the empire, at least for the moment, isn't as weak as they believed.
About the former it's a bit trickier but still doable. With Isaakios not distracted by the Bulgarian uprising, some of the early rebellions of aristocrats and generals (Mangaphas in Philadelphia in 1188, Vranas in Bulgaria in 1187) would be averted, which would give the state a larger degree of stability, really necessary after the disturbances of 1180 - 1185. With the period being mostly peaceful (Isaakios would probably invest more resources trying to reclaim Cyprus if it rebelled - and he could most likely succeed in reclaiming it, but the expenses there would most likely be significantly lower than those incurred by raising armies to suppress the Bulgarian and other domestic uprisings), it is possible that Theodoros Kastamonites, the man who seems to have been responsible for the whole civilian - administrative apparatus, could have implemented certain reforms, especially with regard to taxation and probably avoid many of the tax hikes that IOTL characterised Isaakios' rule. If these efforts were mostly successful and Serbia and Hungary seemed to be firmly in the Byzantine camp or at least in favour of Constantinople, then the situation in Bulgaria could be stabilised and the uprising averted.
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