diff --git a/src/ZeroDimensionalArrays.jl b/src/ZeroDimensionalArrays.jl
index cd7a3f1..0741d5c 100644
--- a/src/ZeroDimensionalArrays.jl
+++ b/src/ZeroDimensionalArrays.jl
@@ -63,6 +63,15 @@ function Base.getindex(a::ZeroDimensionalArray)
     a.v
 end
 
+# This method is redundant for correctness, but adding it helps achieve constprop, which
+# helps `only(::ZeroDimensionalArray)` and `last(::ZeroDimensionalArray)`, for example.
+Base.@constprop :aggressive function Base.getindex(a::ZeroDimensionalArray, i::Int)
+    if !isone(i)
+        throw(BoundsError())
+    end
+    a[]
+end
+
 function Base.setindex!(a::Box, x)
     a.v = x
 end
@@ -71,14 +80,6 @@ Base.@nospecializeinfer function Base.isassigned((@nospecialize unused::ZeroDime
     all(isone, i)
 end
 
-function Base.only(a::ZeroDimensionalArray)
-    a[]
-end
-
-function Base.last(a::ZeroDimensionalArray)
-    a[]
-end
-
 function Base.iterate(a::ZeroDimensionalArray)
     (a[], nothing)
 end
diff --git a/test/runtests.jl b/test/runtests.jl
index 31485f8..4e3911b 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -45,6 +45,10 @@ using Aqua: Aqua
             @test Arr(x) == Arr(x)
             @test all(@inferred Arr(x) .== Arr(x))
             @test (@inferred Arr(x) .+ [10, 20]) isa AbstractVector
+            let oob_exception_type = Exception
+                @test_throws oob_exception_type Arr(x)[0]
+                @test_throws oob_exception_type Arr(x)[2]
+            end
         end
     end