diff --git a/src/Nonlinear/ReverseAD/mathoptinterface_api.jl b/src/Nonlinear/ReverseAD/mathoptinterface_api.jl
index 787eb62673..47ee17393d 100644
--- a/src/Nonlinear/ReverseAD/mathoptinterface_api.jl
+++ b/src/Nonlinear/ReverseAD/mathoptinterface_api.jl
@@ -69,6 +69,7 @@ function MOI.initialize(d::NLPEvaluator, requested_features::Vector{Symbol})
             d.data.expressions[k],
             d.subexpression_linearity,
             moi_index_to_consecutive_index,
+            d.want_hess,
         )
         d.subexpressions[k] = subex
         d.subexpression_linearity[k] = subex.linearity
diff --git a/src/Nonlinear/ReverseAD/types.jl b/src/Nonlinear/ReverseAD/types.jl
index 6526a2d461..fc599accb0 100644
--- a/src/Nonlinear/ReverseAD/types.jl
+++ b/src/Nonlinear/ReverseAD/types.jl
@@ -18,12 +18,17 @@ struct _SubexpressionStorage
         expr::Nonlinear.Expression,
         subexpression_linearity,
         moi_index_to_consecutive_index,
+        want_hess::Bool,
     )
         nodes =
             _replace_moi_variables(expr.nodes, moi_index_to_consecutive_index)
         adj = Nonlinear.adjacency_matrix(nodes)
         N = length(nodes)
-        linearity = _classify_linearity(nodes, adj, subexpression_linearity)
+        linearity = if want_hess
+            _classify_linearity(nodes, adj, subexpression_linearity)[1]
+        else
+            NONLINEAR
+        end
         return new(
             nodes,
             adj,
@@ -32,7 +37,7 @@ struct _SubexpressionStorage
             zeros(N),  # partials_storage,
             zeros(N),  # reverse_storage,
             Float64[],
-            linearity[1],
+            linearity,
         )
     end
 end
diff --git a/test/Nonlinear/ReverseAD.jl b/test/Nonlinear/ReverseAD.jl
index 43fbb28b4f..75a11aae66 100644
--- a/test/Nonlinear/ReverseAD.jl
+++ b/test/Nonlinear/ReverseAD.jl
@@ -630,6 +630,20 @@ function test_linearity()
     return
 end
 
+function test_linearity_no_hess()
+    x = MOI.VariableIndex(1)
+    model = Nonlinear.Model()
+    ex = Nonlinear.add_expression(model, :($x + 1))
+    Nonlinear.set_objective(model, ex)
+    evaluator = Nonlinear.Evaluator(model, Nonlinear.SparseReverseMode(), [x])
+    MOI.initialize(evaluator, [:Grad, :Jac])
+    # We initialized without the need for the hessian so
+    # the linearity shouldn't be computed.
+    @test only(evaluator.backend.subexpressions).linearity ==
+          ReverseAD.NONLINEAR
+    return
+end
+
 function test_dual_forward()
     x = MOI.VariableIndex(1)
     y = MOI.VariableIndex(2)