diff --git a/src/sde_default_alg.jl b/src/sde_default_alg.jl
index d084cca8f..d789e5a94 100644
--- a/src/sde_default_alg.jl
+++ b/src/sde_default_alg.jl
@@ -9,12 +9,14 @@ function default_algorithm(prob::DiffEqBase.AbstractSDEProblem{uType,tType,isinp
     alg = RKMilCommute()
   end
 
-  if :stiff ∈ alg_hints
+  is_stiff = :stiff ∈ alg_hints
+  is_stratonovich = :stratonovich ∈ alg_hints
+  if is_stiff || prob.f.mass_matrix !== I
     alg = ImplicitRKMil(autodiff=false)
   end
 
-  if :stratonovich ∈ alg_hints
-    if :stiff ∈ alg_hints
+  if is_stratonovich
+    if is_stiff || prob.f.mass_matrix !== I
       alg = ImplicitRKMil(autodiff=false,interpretation=:stratonovich)
     else
       alg = RKMil(interpretation=:stratonovich)
@@ -22,14 +24,14 @@ function default_algorithm(prob::DiffEqBase.AbstractSDEProblem{uType,tType,isinp
   end
 
   if prob.noise_rate_prototype != nothing || prob.noise != nothing
-    if :stratonovich ∈ alg_hints
-      if :stiff ∈ alg_hints
+    if is_stratonovich
+      if is_stiff || prob.f.mass_matrix !== I
         alg = ImplicitEulerHeun(autodiff=false)
       else
         alg = LambaEulerHeun()
       end
     else
-      if :stiff ∈ alg_hints
+      if is_stiff || prob.f.mass_matrix !== I
         alg = ISSEM(autodiff=false)
       else
         alg = LambaEM()
@@ -38,7 +40,7 @@ function default_algorithm(prob::DiffEqBase.AbstractSDEProblem{uType,tType,isinp
   end
 
   if :additive ∈ alg_hints
-    if :stiff ∈ alg_hints
+    if is_stiff || prob.f.mass_matrix !== I
       alg = SKenCarp(autodiff=false)
     else
       alg = SOSRA()