diff --git a/test/basictests.jl b/test/basictests.jl
index 9741755a4..a9ced32fa 100644
--- a/test/basictests.jl
+++ b/test/basictests.jl
@@ -224,6 +224,9 @@ end
         P1 = Diagonal(s1)
         P2 = Diagonal(s2)
 
+        @test LinearSolve.ComposePreconditioner(P1,nothing) === P1
+        @test LinearSolve.ComposePreconditioner(nothing,P1) === P1
+
         P  = LinearSolve.ComposePreconditioner(P1,P2)
 
         # ComposePreconditioner