diff --git a/src/atoms/MultiplyAtom.jl b/src/atoms/MultiplyAtom.jl
index 6e9bf9f27..e6c2e20d1 100644
--- a/src/atoms/MultiplyAtom.jl
+++ b/src/atoms/MultiplyAtom.jl
@@ -65,9 +65,7 @@ real_convert(::Type{T}, x::AbstractVector) where {T} = SPARSE_VECTOR{T}(x)
 
 function new_conic_form!(context::Context{T}, x::MultiplyAtom) where {T}
     if curvature(x) == NotDcp()
-        error(
-            "[MultiplyAtom] multiplication of two non-constant expressions is not DCP compliant",
-        )
+        throw(DCPViolationError())
     end
     if x.children[1].size == (1, 1) || x.children[2].size == (1, 1)
         # scalar multiplication
diff --git a/src/dcp.jl b/src/dcp.jl
index 86e9b863c..653c75fca 100644
--- a/src/dcp.jl
+++ b/src/dcp.jl
@@ -15,7 +15,9 @@
 # http://web.stanford.edu/~boyd/papers/disc_cvx_prog.html
 #############################################################################
 
-struct DCPViolationError <: Exception end
+# This is a subtype of MOI.UnsupportedError so that non-DCP
+# errors trigger the correct paths in MOI.Test for Convex.Optimizer.
+struct DCPViolationError <: MOI.UnsupportedError end
 
 function Base.showerror(io::IO, ::DCPViolationError)
     return print(
diff --git a/test/MOI_wrapper.jl b/test/MOI_wrapper.jl
index 38299d45f..8a4e4b207 100644
--- a/test/MOI_wrapper.jl
+++ b/test/MOI_wrapper.jl
@@ -44,8 +44,7 @@ function test_runtests()
                 MOI.VariableBasisStatus,
                 MOI.ObjectiveBound,
             ],
-        );
-        exclude = ["hs071"],  # HS071 is not convex
+        ),
     )
     return
 end
diff --git a/test/test_atoms.jl b/test/test_atoms.jl
index 1243f8a3f..f198c7a02 100644
--- a/test/test_atoms.jl
+++ b/test/test_atoms.jl
@@ -660,15 +660,11 @@ function test_MultiplyAtom()
         Variable(2, 2) * Variable(3, 3)
     )
     @test_throws(
-        ErrorException(
-            "[MultiplyAtom] multiplication of two non-constant expressions is not DCP compliant",
-        ),
+        DCPViolationError,
         _test_atom(_ -> Variable(2)' * Variable(2), ""),
     )
     @test_throws(
-        ErrorException(
-            "[MultiplyAtom] multiplication of two non-constant expressions is not DCP compliant",
-        ),
+        DCPViolationError,
         _test_atom(_ -> Variable() * Variable(), ""),
     )
     return