diff --git a/.github/workflows/Tests.yml b/.github/workflows/Tests.yml
index 7a27a1d9e..978d8d18e 100644
--- a/.github/workflows/Tests.yml
+++ b/.github/workflows/Tests.yml
@@ -38,10 +38,17 @@ jobs:
           - "NoPre"
           - "LinearSolveAutotune"
           - "Preferences"
+          - "Trim"
         os:
           - ubuntu-latest
           - macos-latest
           - windows-latest
+        exclude:
+          # Don't run trim tests on Julia versions below 1.12
+          - group: Trim
+            version: "lts"
+          - group: Trim
+            version: "pre"
     uses: "SciML/.github/.github/workflows/tests.yml@v1"
     with:
       group: "${{ matrix.group }}"
diff --git a/Project.toml b/Project.toml
index 7f89526d8..5f386a640 100644
--- a/Project.toml
+++ b/Project.toml
@@ -41,13 +41,13 @@ EnzymeCore = "f151be2c-9106-41f4-ab19-57ee4f262869"
 FastAlmostBandedMatrices = "9d29842c-ecb8-4973-b1e9-a27b1157504e"
 FastLapackInterface = "29a986be-02c6-4525-aec4-84b980013641"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
-Mooncake = "da2b9cff-9c12-43a0-ae48-6db2b0edb7d6"
 HYPRE = "b5ffcf37-a2bd-41ab-a3da-4bd9bc8ad771"
 IterativeSolvers = "42fd0dbc-a981-5370-80f2-aaf504508153"
 KernelAbstractions = "63c18a36-062a-441e-b654-da1e3ab1ce7c"
 KrylovKit = "0b1a1467-8014-51b9-945f-bf0ae24f4b77"
 LAPACK_jll = "51474c39-65e3-53ba-86ba-03b1b862ec14"
 Metal = "dde4c033-4e86-420c-a63e-0dd931031962"
+Mooncake = "da2b9cff-9c12-43a0-ae48-6db2b0edb7d6"
 Pardiso = "46dd5b70-b6fb-5a00-ae2d-e8fea33afaf2"
 RecursiveFactorization = "f2c3362d-daeb-58d1-803e-2bc74f2840b4"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
@@ -90,8 +90,8 @@ CUDSS = "0.4, 0.6.1"
 CUSOLVERRF = "0.2.6"
 ChainRulesCore = "1.25"
 CliqueTrees = "1.11.0"
-ConcreteStructs = "0.2.3"
 ComponentArrays = "0.15.29"
+ConcreteStructs = "0.2.3"
 DocStringExtensions = "0.9.3"
 EnumX = "1.0.4"
 EnzymeCore = "0.8.5"
@@ -129,8 +129,8 @@ RecursiveFactorization = "0.2.26"
 Reexport = "1.2.2"
 SafeTestsets = "0.1"
 SciMLBase = "2.70"
-SciMLOperators = "1.7.1"
 SciMLLogging = "1.3.1"
+SciMLOperators = "1.7.1"
 Setfield = "1.1.1"
 SparseArrays = "1.10"
 Sparspak = "0.3.9"
@@ -163,13 +163,13 @@ KrylovKit = "0b1a1467-8014-51b9-945f-bf0ae24f4b77"
 KrylovPreconditioners = "45d422c2-293f-44ce-8315-2cb988662dec"
 MPI = "da04e1cc-30fd-572f-bb4f-1f8673147195"
 Metal = "dde4c033-4e86-420c-a63e-0dd931031962"
+Mooncake = "da2b9cff-9c12-43a0-ae48-6db2b0edb7d6"
 MultiFloats = "bdf0d083-296b-4888-a5b6-7498122e68a5"
 Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 RecursiveArrayTools = "731186ca-8d62-57ce-b412-fbd966d074cd"
 RecursiveFactorization = "f2c3362d-daeb-58d1-803e-2bc74f2840b4"
 SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
-Mooncake = "da2b9cff-9c12-43a0-ae48-6db2b0edb7d6"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 Sparspak = "e56a9233-b9d6-4f03-8d0f-1825330902ac"
 StableRNGs = "860ef19b-820b-49d6-a774-d7a799459cd3"
diff --git a/test/runtests.jl b/test/runtests.jl
index 2d2b5dc2e..15ab5554d 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -73,3 +73,10 @@ end
 if Base.Sys.islinux() && (GROUP == "All" || GROUP == "LinearSolveHYPRE") && HAS_EXTENSIONS
     @time @safetestset "LinearSolveHYPRE" include("hypretests.jl")
 end
+
+if GROUP == "Trim" && VERSION >= v"1.12.0"
+    Pkg.activate("trim")
+    Pkg.develop(PackageSpec(path = dirname(@__DIR__)))
+    Pkg.instantiate()
+    @time @safetestset "Trim Tests" include("trim/runtests.jl")
+end
diff --git a/test/trim/Project.toml b/test/trim/Project.toml
new file mode 100644
index 000000000..bdde4ead0
--- /dev/null
+++ b/test/trim/Project.toml
@@ -0,0 +1,25 @@
+name = "TrimTest"
+uuid = "e59a8f5e-4b8c-4d8e-9c8e-8e8e8e8e8e8e"
+version = "0.1.0"
+
+[deps]
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+LinearSolve = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
+RecursiveFactorization = "f2c3362d-daeb-58d1-803e-2bc74f2840b4"
+SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
+StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
+Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+
+[extras]
+JET = "c3a54625-cd67-489e-a8e7-0a5a0ff4e31b"
+SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
+
+[targets]
+test = ["JET", "SafeTestsets"]
+
+[compat]
+LinearSolve = "3"
+RecursiveFactorization = "0.2"
+SciMLBase = "2"
+StaticArrays = "1"
+julia = "1.10"
diff --git a/test/trim/linear_lu.jl b/test/trim/linear_lu.jl
new file mode 100644
index 000000000..733f2e6e8
--- /dev/null
+++ b/test/trim/linear_lu.jl
@@ -0,0 +1,22 @@
+module TestLUFactorization
+using LinearSolve
+using LinearAlgebra
+using StaticArrays
+import SciMLBase
+
+# Define a simple linear problem with a dense matrix
+const A_matrix = [4.0 1.0; 1.0 3.0]
+const b_vector = [1.0, 2.0]
+
+const alg = LUFactorization()
+const prob = LinearProblem(A_matrix, b_vector)
+const cache = init(prob, alg)
+
+function solve_linear(x)
+    # Create a new problem with a modified b vector
+    b_new = [x, 2.0 * x]
+    reinit!(cache; b = b_new)
+    sol = solve!(cache)
+    return sol
+end
+end
diff --git a/test/trim/linear_mkl.jl b/test/trim/linear_mkl.jl
new file mode 100644
index 000000000..76b20c386
--- /dev/null
+++ b/test/trim/linear_mkl.jl
@@ -0,0 +1,22 @@
+module TestMKLLUFactorization
+using LinearSolve
+using LinearAlgebra
+using StaticArrays
+import SciMLBase
+
+# Define a simple linear problem with a dense matrix
+const A_matrix = [4.0 1.0; 1.0 3.0]
+const b_vector = [1.0, 2.0]
+
+const alg = MKLLUFactorization()
+const prob = LinearProblem(A_matrix, b_vector)
+const cache = init(prob, alg)
+
+function solve_linear(x)
+    # Create a new problem with a modified b vector
+    b_new = [x, 2.0 * x]
+    reinit!(cache; b = b_new)
+    sol = solve!(cache)
+    return sol
+end
+end
diff --git a/test/trim/linear_rf.jl b/test/trim/linear_rf.jl
new file mode 100644
index 000000000..fb90403a1
--- /dev/null
+++ b/test/trim/linear_rf.jl
@@ -0,0 +1,23 @@
+module TestRFLUFactorization
+using LinearSolve
+using LinearAlgebra
+using StaticArrays
+using RecursiveFactorization
+import SciMLBase
+
+# Define a simple linear problem with a dense matrix
+const A_matrix = [4.0 1.0; 1.0 3.0]
+const b_vector = [1.0, 2.0]
+
+const alg = RFLUFactorization()
+const prob = LinearProblem(A_matrix, b_vector)
+const cache = init(prob, alg)
+
+function solve_linear(x)
+    # Create a new problem with a modified b vector
+    b_new = [x, 2.0 * x]
+    reinit!(cache; b = b_new)
+    sol = solve!(cache)
+    return sol
+end
+end
diff --git a/test/trim/main_lu.jl b/test/trim/main_lu.jl
new file mode 100644
index 000000000..3bc97767e
--- /dev/null
+++ b/test/trim/main_lu.jl
@@ -0,0 +1,8 @@
+using TrimTest
+
+function (@main)(argv::Vector{String})::Cint
+    x = parse(Float64, argv[1])
+    sol = TrimTest.TestLUFactorization.solve_linear(x)
+    println(Core.stdout, sum(sol.u))
+    return 0
+end
diff --git a/test/trim/main_mkl.jl b/test/trim/main_mkl.jl
new file mode 100644
index 000000000..c2a1128f2
--- /dev/null
+++ b/test/trim/main_mkl.jl
@@ -0,0 +1,8 @@
+using TrimTest
+
+function (@main)(argv::Vector{String})::Cint
+    x = parse(Float64, argv[1])
+    sol = TrimTest.TestMKLLUFactorization.solve_linear(x)
+    println(Core.stdout, sum(sol.u))
+    return 0
+end
diff --git a/test/trim/main_rf.jl b/test/trim/main_rf.jl
new file mode 100644
index 000000000..e16e7e67c
--- /dev/null
+++ b/test/trim/main_rf.jl
@@ -0,0 +1,8 @@
+using TrimTest
+
+function (@main)(argv::Vector{String})::Cint
+    x = parse(Float64, argv[1])
+    sol = TrimTest.TestRFLUFactorization.solve_linear(x)
+    println(Core.stdout, sum(sol.u))
+    return 0
+end
diff --git a/test/trim/runtests.jl b/test/trim/runtests.jl
new file mode 100644
index 000000000..d26228281
--- /dev/null
+++ b/test/trim/runtests.jl
@@ -0,0 +1,87 @@
+using SafeTestsets
+
+@safetestset "LUFactorization implementation" begin
+    using LinearAlgebra
+    include("linear_lu.jl")
+    sol = TestLUFactorization.solve_linear(1.0)
+    @test sol.u ≈ [0.09090909090909091, 0.6363636363636364]
+end
+
+@safetestset "MKLLUFactorization implementation" begin
+    using LinearAlgebra
+    using LinearSolve
+    # Only test if MKL is available
+    if LinearSolve.usemkl
+        include("linear_mkl.jl")
+        sol = TestMKLLUFactorization.solve_linear(1.0)
+        @test sol.u ≈ [0.09090909090909091, 0.6363636363636364]
+    else
+        @test_skip "MKL not available"
+    end
+end
+
+@safetestset "RFLUFactorization implementation" begin
+    using LinearAlgebra
+    include("linear_rf.jl")
+    sol = TestRFLUFactorization.solve_linear(1.0)
+    @test sol.u ≈ [0.09090909090909091, 0.6363636363636364]
+end
+
+@safetestset "Run trim" begin
+    # https://discourse.julialang.org/t/capture-stdout-and-stderr-in-case-a-command-fails/101772/3?u=romeov
+    """
+    Run a Cmd object, returning the stdout & stderr contents plus the exit code
+    """
+    function _execute(cmd::Cmd)
+        out = Pipe()
+        err = Pipe()
+        process = run(pipeline(ignorestatus(cmd); stdout = out, stderr = err))
+        close(out.in)
+        close(err.in)
+        out = (
+            stdout = String(read(out)), stderr = String(read(err)),
+            exitcode = process.exitcode
+        )
+        return out
+    end
+
+    JULIAC = normpath(
+        joinpath(
+        Sys.BINDIR, Base.DATAROOTDIR, "julia", "juliac",
+        "juliac.jl"
+    )
+    )
+    @test isfile(JULIAC)
+
+    using LinearSolve
+    # Build list of tests to run, conditionally including MKL
+    test_files = [
+        ("main_lu.jl", true),
+        ("main_rf.jl", true)
+    ]
+    if LinearSolve.usemkl
+        push!(test_files, ("main_mkl.jl", true))
+    end
+
+    for (mainfile, expectedtopass) in test_files
+        binpath = tempname()
+        cmd = `$(Base.julia_cmd()) --project=. --depwarn=error $(JULIAC) --experimental --trim=unsafe-warn --output-exe $(binpath) $(mainfile)`
+
+        # since we are calling Julia from Julia, we first need to clean some
+        # environment variables
+        clean_env = copy(ENV)
+        delete!(clean_env, "JULIA_PROJECT")
+        delete!(clean_env, "JULIA_LOAD_PATH")
+        # We could just check for success, but then failures are hard to debug.
+        # Instead we use `_execute` to also capture `stdout` and `stderr`.
+        # @test success(setenv(cmd, clean_env))
+        trimcall = _execute(setenv(cmd, clean_env; dir = @__DIR__))
+        if trimcall.exitcode != 0 && expectedtopass
+            @show trimcall.stdout
+            @show trimcall.stderr
+        end
+        @test trimcall.exitcode == 0 broken = !expectedtopass
+        @test isfile(binpath) broken = !expectedtopass
+        @test success(`$(binpath) 1.0`) broken = !expectedtopass
+    end
+end
diff --git a/test/trim/src/TrimTest.jl b/test/trim/src/TrimTest.jl
new file mode 100644
index 000000000..ad9e43be6
--- /dev/null
+++ b/test/trim/src/TrimTest.jl
@@ -0,0 +1,7 @@
+module TrimTest
+
+include("../linear_lu.jl")
+include("../linear_mkl.jl")
+include("../linear_rf.jl")
+
+end