diff --git a/HISTORY.md b/HISTORY.md
index 026c849d..2a51050d 100644
--- a/HISTORY.md
+++ b/HISTORY.md
@@ -1,3 +1,7 @@
+## 0.13.4
+
+Added missing methods for `subsumes(::IndexLens, ::PropertyLens)` and vice versa.
+
 ## 0.13.3
 
 Bumped compatibility for JSON.jl to include v1.
diff --git a/Project.toml b/Project.toml
index 471a9b3b..d061d430 100644
--- a/Project.toml
+++ b/Project.toml
@@ -3,7 +3,7 @@ uuid = "7a57a42e-76ec-4ea3-a279-07e840d6d9cf"
 keywords = ["probablistic programming"]
 license = "MIT"
 desc = "Common interfaces for probabilistic programming"
-version = "0.13.3"
+version = "0.13.4"
 
 [deps]
 AbstractMCMC = "80f14c24-f653-4e6a-9b94-39d6b0f70001"
diff --git a/src/varname/subsumes.jl b/src/varname/subsumes.jl
index 0af5cb4a..f43a92b4 100644
--- a/src/varname/subsumes.jl
+++ b/src/varname/subsumes.jl
@@ -103,6 +103,10 @@ subsumes(t::PropertyLens{name}, u::PropertyLens{name}) where {name} = true
 # Otherwise they represent different properties, and thus are not the same.
 subsumes(t::PropertyLens, u::PropertyLens) = false
 
+# PropertyLens and IndexLens can't subsume each other
+subsumes(::PropertyLens, ::IndexLens) = false
+subsumes(::IndexLens, ::PropertyLens) = false
+
 # Indices subsumes if they are subindices, i.e. we just call `_issubindex`.
 # FIXME: Does not support `DynamicIndexLens`.
 # FIXME: Does not correctly handle cases such as `subsumes(x, x[:])`
diff --git a/test/varname.jl b/test/varname.jl
index c4895e79..ebf19b59 100644
--- a/test/varname.jl
+++ b/test/varname.jl
@@ -126,7 +126,9 @@ end
         @test @varname(x) ≍ @varname(y)
         @test @varname(x.a) ≍ @varname(y.a)
         @test @varname(a.x) ≍ @varname(a.y)
+        @test @varname(a.x[1]) ≍ @varname(a.x.z)
         @test @varname(x[1]) ≍ @varname(y[1])
+        @test @varname(x[1]) ≍ @varname(x.y)
 
         # x ∘ ℓ ⊑ x
         @test_strict_subsumption x.a x