diff --git a/src/utils.jl b/src/utils.jl
index 0209140a..cee9f79e 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -86,6 +86,7 @@ function recursivecopy!(
         T2 <: StaticArraysCore.StaticArray,
         N,
     }
+    checkbounds(b, eachindex(a))
     return @inbounds for i in eachindex(a)
         # TODO: Check for `setindex!`` and use `copy!(b[i],a[i])` or `b[i] = a[i]`, see #19
         b[i] = copy(a[i])
@@ -355,8 +356,9 @@ end
 """
     copyat_or_push!(a, i, x[, perform_copy = true]) -> nothing
 
-Recursively copy `x` into `a[i]` when that element exists, or append a recursive copy
-of `x` otherwise. Set `perform_copy = false` to assign or append `x` directly.
+Recursively copy `x` into `a[i]` when `i` is an index of `a`, or append a recursive copy
+of `x` when `i > lastindex(a)`. Set `perform_copy = false` to assign or append `x`
+directly. Throws a `BoundsError` when `i < firstindex(a)`.
 
 # Examples
 
@@ -367,8 +369,9 @@ values == [[1, 2], [3, 4]]
 ```
 """
 function copyat_or_push!(a::AbstractVector{T}, i::Int, x, perform_copy = true) where {T}
-    @inbounds if length(a) >= i
-        if !ArrayInterface.ismutable(T) || !perform_copy
+    i >= firstindex(a) || throw(BoundsError(a, i))
+    if i <= lastindex(a)
+        @inbounds if !ArrayInterface.ismutable(T) || !perform_copy
             # TODO: Check for `setindex!`` if T <: StaticArraysCore.StaticArray and use `copy!(b[i],a[i])`
             #       or `b[i] = a[i]`, see https://github.com/JuliaDiffEq/RecursiveArrayTools.jl/issues/19
             a[i] = x
diff --git a/test/Core/utils_test.jl b/test/Core/utils_test.jl
index 3ef3bb0c..bef70ec5 100644
--- a/test/Core/utils_test.jl
+++ b/test/Core/utils_test.jl
@@ -2,6 +2,19 @@ using RecursiveArrayTools, StaticArrays
 using RecursiveArrayToolsShorthandConstructors
 using Test
 
+# A vector whose indices start at `first`, like an `OffsetArrays.OffsetVector`:
+# `OffsetVec(v, 0)` has axes `0:length(v)-1`.
+struct OffsetVec{T} <: AbstractVector{T}
+    data::Vector{T}
+    first::Int
+end
+Base.axes(o::OffsetVec) = (o.first:(o.first + length(o.data) - 1),)
+Base.size(o::OffsetVec) = size(o.data)
+Base.getindex(o::OffsetVec, i::Int) = o.data[i - o.first + 1]
+Base.setindex!(o::OffsetVec, v, i::Int) = (o.data[i - o.first + 1] = v)
+Base.push!(o::OffsetVec, v) = (push!(o.data, v); o)
+Base.IndexStyle(::Type{<:OffsetVec}) = IndexLinear()
+
 t = collect(range(0, stop = 10, length = 200))
 randomized = VectorOfArray([0.01randn(2) for i in 1:10])
 data = convert(Array, randomized)
@@ -152,6 +165,55 @@ end
     @test a.u[1][1] == 1.0
 end
 
+@testset "recursivecopy! of StaticArray elements checks destination bounds" begin
+    a = [MVector{2, Float64}(1, 1), MVector{2, Float64}(2, 2)]
+    shorter = [MVector{2, Float64}(0, 0)]
+    @test_throws BoundsError recursivecopy!(shorter, a)
+    @test all(iszero, shorter)
+    offset = OffsetVec([MVector{2, Float64}(0, 0) for _ in 1:2], 0)
+    @test_throws BoundsError recursivecopy!(offset, a)
+    @test all(iszero, offset.data)
+    @test_throws BoundsError recursivecopy!(zeros(SVector{2, Float64}, 2, 2), fill(SVector(1.0, 1.0), 3, 3))
+
+    longer = [MVector{2, Float64}(0, 0) for _ in 1:3]
+    recursivecopy!(longer, a)
+    @test longer == [[1, 1], [2, 2], [0, 0]]
+    @test longer[1] !== a[1]
+
+    b = [MVector{2, Float64}(0, 0), MVector{2, Float64}(0, 0)]
+    recursivecopy!(b, a)
+    @test b == a
+    @test b[1] !== a[1]
+end
+
+@testset "copyat_or_push! uses the indices of the destination" begin
+    vals = [[1, 2], [3, 4]]
+    @test_throws BoundsError copyat_or_push!(vals, 0, [9, 9])
+    @test_throws BoundsError copyat_or_push!(vals, -1, [9, 9])
+    @test vals == [[1, 2], [3, 4]]
+    copyat_or_push!(vals, 1, [9, 9])
+    @test vals == [[9, 9], [3, 4]]
+    copyat_or_push!(vals, 3, [5, 6])
+    @test vals == [[9, 9], [3, 4], [5, 6]]
+
+    z = OffsetVec([[1, 2], [3, 4]], 0)
+    @test_throws BoundsError copyat_or_push!(z, -1, [9, 9])
+    copyat_or_push!(z, 0, [9, 9])
+    @test z.data == [[9, 9], [3, 4]]
+    copyat_or_push!(z, 2, [5, 6])
+    @test z.data == [[9, 9], [3, 4], [5, 6]]
+
+    o = OffsetVec([[1, 2], [3, 4]], 2)
+    @test_throws BoundsError copyat_or_push!(o, 1, [9, 9])
+    copyat_or_push!(o, 3, [8, 8])
+    @test o.data == [[1, 2], [8, 8]]
+    x = [7, 7]
+    copyat_or_push!(o, 2, x, false)
+    @test o.data[1] === x
+    copyat_or_push!(o, 4, [5, 6])
+    @test o.data == [[7, 7], [8, 8], [5, 6]]
+end
+
 # OrdinaryDiffEq.jl#1365: recursivecopy must not broadcast-assign into an
 # immutable outer container such as SVector of arrays.
 @testset "recursivecopy VectorOfArray with SVector outer (ODE#1365)" begin