  We provide a new sequent calculus that enjoys syntactic cut-elimination and
strongly terminating backward proof search for the intuitionistic Strong L\"ob
logic $\sf{iSL}$, an intuitionistic modal logic with a provability
interpretation. A novel measure on sequents is used to prove both the
termination of the naive backward proof search strategy, and the admissibility
of cut in a syntactic and direct way, leading to a straightforward
cut-elimination procedure. All proofs have been formalised in the interactive
theorem prover Coq.
