According to so-called epistemic theories of conditionals, the assertability/ acceptability/acceptance of a conditional requires the existence of an epistemically significant relation between the conditional's antecedent and its consequent. This paper points to some linguistic data that our current best theories of the foregoing type appear unable to explain. Further, it presents a new theory of the same type that does not have that shortcoming. The theory is then defended against some seemingly obvious objections.Keywords Conditionals · Probability · Semantics · Bayesian epistemology According to so-called epistemic theories of conditionals, the assertability/acceptability/acceptance of a conditional requires the existence of an epistemically relevant relation between the conditional's antecedent and its consequent. It is the working hypothesis of this paper that some such theory is correct at least for indicative conditionals. However, below I will point to some linguistic data that our current best epistemic theories of conditionals appear unable to explain. I further present a new theory of the same type that does not have that shortcoming and that also seems to withstand further scrutiny.As a preliminary point, I should note that the present paper's main focus will be on simple indicative conditionals, that is, indicative conditionals the antecedents and consequents of which do not contain conditionals, and then chiefly on the assertability/ acceptability conditions of those conditionals, and not so much on their truth conditions (if they have any). Also, I will leave compounds of conditionals undiscussed. This is not much of an omission if those are right who have argued that a substantial part of the embedded conditionals we encounter in daily speech can be reduced to I. Douven (B)