diff --git a/src/scalar.jl b/src/scalar.jl
index 9d13d0f6..4e551714 100644
--- a/src/scalar.jl
+++ b/src/scalar.jl
@@ -379,16 +379,14 @@ end
 for T in SCALINGNUMBERTYPES[2:end]
     @eval function Base.:*(α::ScalarOperator, x::$T)
         if isconstant(α)
-            T2 = promote_type($T, eltype(α))
-            return ScalarOperator(convert(T2, α) * x, α.update_func)
+            return ScalarOperator(concretize(α) * x)
         else
             return ComposedScalarOperator(α, ScalarOperator(x))
         end
     end
     @eval function Base.:*(x::$T, α::ScalarOperator)
         if isconstant(α)
-            T2 = promote_type($T, eltype(α))
-            return ScalarOperator(convert(T2, α) * x, α.update_func)
+            return ScalarOperator(concretize(α) * x)
         else
             return ComposedScalarOperator(ScalarOperator(x), α)
         end
diff --git a/test/scalar.jl b/test/scalar.jl
index a0a7b06b..c4a8bc35 100644
--- a/test/scalar.jl
+++ b/test/scalar.jl
@@ -74,6 +74,11 @@ K = 12
     copy!(w, orig_w)
     α(w, v, u, nothing, 0.0, a, b)
     @test w ≈ a * (x * v) + b * orig_w
+
+    # Operations with UniformScalar
+    α = ScalarOperator(1)
+    @test α * I == α
+    @test α + I isa AddedScalarOperator
 end
 
 @testset "ScalarOperator Combinations" begin