An operator ∗→ is said to be Boethian in a logic L iff it is either primitive or defined inLand (i)Lcontains the so-called Boethius’ Thesis A ∗→B ⊃ ¬(A ∗→¬B); (ii) the wffs (A ⊃ B) ⊃ A ∗→B and A ∗→B ⊃ B ∗→A are not L-theorems. The aim of the paper is to show how a Boethian operator may be generated by suitable definitions from non-Boethian operators such as strict implication (J) and Stalnaker-Lewis conditional (>). The schemata of the two proposed definitions are A⇝B =df A J B & δ and A +→B =df A > B & δ where δ is a wff in the two sets Ant = {A, ¬A,□A,□¬A, ♢A, ♢¬A} or Cons = {B, ¬B,□B,□¬B, ♢B, ♢¬B}. It is proved that, if the background system for strict implication is the modal system KD, the only modal instance of δ which grants the properties of a Boethian operator is the wff ♢A. A drawback of this definition of ⇝ is that it does not allows proving Identity, i.e. A⇝A. In order to justify Identity a more refined analysis requires that the values of δ be chosen not only in Ant and Cons but also in the set of disjunctive wffs {B ∨ ♢A, ¬B ∨ ♢A, ♢B ∨ ♢A, ♢¬B ∨ ♢A,□¬B ∨ ♢A,□B ∨ ♢A}. It turns out that in this set the only two values of δ which yield Boethian operators are □¬B ∨ ♢A and □B ∨ ♢A. The former turns out to be equivalent to a consequential operator axiomatized in Pizzi [7], the latter is equivalent to another one which has been axiomatized in Lowe [4]. It is proved in section 4.6 that the former is the only value of δ that grants Identity. In the second part of the paper the same schema of analysis is applied to Lewis’ conditional operator >, while the background system is the conditional system VW−. It turns out that the modal values of δ in Ant and Cons which allow defining a Boethian operator +→ are not only ♢A but also □A and □B. Given that all them fail to grant Identity, the values of δ must again be chosen in a set of disjunctive statements, which however is wider than the one for ⇝. For both ⇝and +→ an investigation is performed in sections 4.7 and 4.8 aiming to see which special cases of ⇝ and +→ satisfy the following properties: Aristotle’s Thesis, Simplification, Secondary Boethius, Transitivity, Contraposition, Monotonicity.