diff --git a/src/algorithms/derivatives/hamiltonian_derivatives.jl b/src/algorithms/derivatives/hamiltonian_derivatives.jl
index 47ee2b25a..438fe87ec 100644
--- a/src/algorithms/derivatives/hamiltonian_derivatives.jl
+++ b/src/algorithms/derivatives/hamiltonian_derivatives.jl
@@ -199,6 +199,15 @@ function AC2_hamiltonian(
     return prepare ? prepare_operator!!(H_AC2) : H_AC2
 end
 
+for f in (:AC_hamiltonian, :AC2_hamiltonian)
+    @eval function $f(
+            site::Int, below::WindowMPS, operator::WindowMPOHamiltonian, above::WindowMPS,
+            envs; kwargs...
+        )
+        return $f(site, below, operator.finite_ham, above, envs; kwargs...)
+    end
+end
+
 function JordanMPO_AC2_Hamiltonian(GL::MPSTensor, W1::JordanMPOTensor, W2::JordanMPOTensor, GR::MPSTensor)
     # block accessors recompute a fresh `SparseBlockTensorMap` on every access, so bind
     # them once and reuse the locals throughout
diff --git a/src/operators/windowhamiltonian.jl b/src/operators/windowhamiltonian.jl
index f4ace7c45..a0833aa56 100644
--- a/src/operators/windowhamiltonian.jl
+++ b/src/operators/windowhamiltonian.jl
@@ -44,6 +44,7 @@ end
 
 Base.parent(h::WindowMPOHamiltonian) = h.finite_ham
 Base.copy(h::WindowMPOHamiltonian) = WindowMPOHamiltonian(copy(h.left_ham), copy(h.finite_ham), copy(h.right_ham))
+Base.conj(h::WindowMPOHamiltonian) = WindowMPOHamiltonian(conj(h.left_ham), conj(h.finite_ham), conj(h.right_ham))
 
 function Base.:+(a::WindowMPOHamiltonian, b::WindowMPOHamiltonian)
     # the finite window carries full Jordan virtual spaces at its boundaries, so it has to be