diff --git a/.github/workflows/downstream.yml b/.github/workflows/downstream.yml
new file mode 100644
index 0000000..1f93564
--- /dev/null
+++ b/.github/workflows/downstream.yml
@@ -0,0 +1,68 @@
+name: IntegrationTest
+on:
+  push:
+    branches: [master]
+    tags: [v*]
+  pull_request:
+    paths-ignore:
+      - 'LICENSE'
+      - 'README.md'
+      - '.github/workflows/TagBot.yml'
+
+jobs:
+  pre_job:
+    # continue-on-error: true # Uncomment once integration is finished
+    runs-on: ubuntu-latest
+    # Map a step output to a job output
+    outputs:
+      should_skip: ${{ steps.skip_check.outputs.should_skip }}
+    steps:
+      - id: skip_check
+        uses: fkirc/skip-duplicate-actions@v5
+  test:
+    needs: pre_job
+    if: needs.pre_job.outputs.should_skip != 'true'
+    name: ${{ matrix.package.group }}/${{ matrix.package.repo }}/${{ matrix.julia-version }}
+    runs-on: ${{ matrix.os }}
+    strategy:
+      fail-fast: false
+      matrix:
+        julia-version: ['1']
+        os: [ubuntu-latest]
+        package:
+          - {repo: ClassicalOrthogonalPolynomials.jl, group: JuliaApproximation}
+          - {repo: MultivariateOrthogonalPolynomials.jl, group: JuliaApproximation}
+    steps:
+      - uses: actions/checkout@v4
+      - uses: julia-actions/setup-julia@v2
+        with:
+          version: ${{ matrix.julia-version }}
+          arch: x64
+      - uses: julia-actions/julia-buildpkg@latest
+      - name: Clone Downstream
+        uses: actions/checkout@v4
+        with:
+          repository: ${{ matrix.package.group }}/${{ matrix.package.repo }}
+          path: downstream
+      - name: Load this and run the downstream tests
+        shell: julia --color=yes --project=downstream {0}
+        run: |
+          using Pkg
+          try
+            # force it to use this PR's version of the package
+            Pkg.develop(PackageSpec(path="."))  # resolver may fail with main deps
+            Pkg.update()
+            Pkg.test(; coverage = true)  # resolver may fail with test time deps
+          catch err
+            err isa Pkg.Resolve.ResolverError || rethrow()
+            # If we can't resolve that means this is incompatible by SemVer and this is fine
+            # It means we marked this as a breaking change, so we don't need to worry about
+            # Mistakenly introducing a breaking change, as we have intentionally made one
+            @info "Not compatible with this release. No problem." exception=err
+            exit(0)  # Exit immediately, as a success
+          end
+      - uses: julia-actions/julia-processcoverage@v1
+      - uses: codecov/codecov-action@v5
+        with:
+          token: ${{ secrets.CODECOV_TOKEN }}
+          files: lcov.info
diff --git a/Project.toml b/Project.toml
index 49951bc..af9c2b2 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "InfiniteLinearAlgebra"
 uuid = "cde9dba0-b1de-11e9-2c62-0bab9446c55c"
-version = "0.9.0"
+version = "0.9.1"
 
 [deps]
 ArrayLayouts = "4c555306-a7a7-4459-81d9-ec55ddd5c99a"
diff --git a/src/infcholesky.jl b/src/infcholesky.jl
index e49268e..6292579 100644
--- a/src/infcholesky.jl
+++ b/src/infcholesky.jl
@@ -54,7 +54,8 @@ ArrayLayouts._cholesky(::SymTridiagonalLayout, ::NTuple{2,OneToInf{Int}}, A, ::C
 ArrayLayouts._cholesky(::SymmetricLayout{<:AbstractBandedLayout}, ::NTuple{2,OneToInf{Int}}, A, ::CNoPivot) = adaptivecholesky(A)
 
 colsupport(::AdaptiveCholeskyFactors, ::OneToInf) = OneToInf()
-rowsupport(::AdaptiveCholeskyFactors, ::OneToInf) = OneToInf()
+colsupport(F::AdaptiveCholeskyFactors, kr::AbstractInfUnitRange) = max(1,kr[1]-bandwidth(F,2)):∞
+rowsupport(::AdaptiveCholeskyFactors, kr::AbstractInfUnitRange) = kr
 
 function colsupport(F::AdaptiveCholeskyFactors, j)
     partialcholesky!(F, maximum(j)+bandwidth(F,2))
diff --git a/test/test_infcholesky.jl b/test/test_infcholesky.jl
index bebae6b..5300b15 100644
--- a/test/test_infcholesky.jl
+++ b/test/test_infcholesky.jl
@@ -64,6 +64,9 @@ import InfiniteLinearAlgebra: SymmetricBandedLayouts, AdaptiveCholeskyFactors
         F = cholesky(S)
         @test colsupport(F.factors,5) == rowsupport(F.factors,3) == 3:5
         @test rowsupport(F.factors) == colsupport(F.factors) == axes(F.factors,1)
+        @test rowsupport(F.factors,2:∞) == 2:∞
+        @test colsupport(F.factors,2:∞) == 1:∞
+        @test colsupport(F.factors,5:∞) == 3:∞
 
         @test (F.U * F.U')[1:10,1:10]  ≈ F.U[1:10,1:12] * F.U[1:10,1:12]'
         @test (F.U' * F.U)[1:10,1:10]  ≈ S[1:10,1:10]