diff --git a/Project.toml b/Project.toml
index 78702565..254377c9 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "MatrixAlgebraKit"
 uuid = "6c742aac-3347-4629-af66-fc926824e5e4"
 authors = ["Jutho <jutho.haegeman@ugent.be> and contributors"]
-version = "0.1.1"
+version = "0.1.2"
 
 [deps]
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
diff --git a/src/implementations/truncation.jl b/src/implementations/truncation.jl
index f135df10..6088ed7e 100644
--- a/src/implementations/truncation.jl
+++ b/src/implementations/truncation.jl
@@ -11,10 +11,17 @@ function TruncationStrategy(; atol=nothing, rtol=nothing, maxrank=nothing)
     if isnothing(maxrank) && isnothing(atol) && isnothing(rtol)
         return NoTruncation()
     elseif isnothing(maxrank)
-        @assert isnothing(rtol) "TODO: rtol"
-        return trunctol(atol)
+        atol = @something atol 0
+        rtol = @something rtol 0
+        return TruncationKeepAbove(atol, rtol)
     else
-        return truncrank(maxrank)
+        if isnothing(atol) && isnothing(rtol)
+            return truncrank(maxrank)
+        else
+            atol = @something atol 0
+            rtol = @something rtol 0
+            return truncrank(maxrank) & TruncationKeepAbove(atol, rtol)
+        end
     end
 end
 
@@ -82,6 +89,28 @@ Truncation strategy to discard the values that are larger than `atol` in absolut
 """
 truncabove(atol) = TruncationKeepFiltered(≤(atol) ∘ abs)
 
+"""
+    TruncationIntersection(trunc1::TruncationStrategy, trunc2::TruncationStrategy)
+
+Compose two truncation strategies, keeping values common between the two strategies.
+"""
+struct TruncationIntersection{T<:Tuple{Vararg{TruncationStrategy}}} <:
+       TruncationStrategy
+    components::T
+end
+function Base.:&(trunc1::TruncationStrategy, trunc2::TruncationStrategy)
+    return TruncationIntersection((trunc1, trunc2))
+end
+function Base.:&(trunc1::TruncationIntersection, trunc2::TruncationIntersection)
+    return TruncationIntersection((trunc1.components..., trunc2.components...))
+end
+function Base.:&(trunc1::TruncationIntersection, trunc2::TruncationStrategy)
+    return TruncationIntersection((trunc1.components..., trunc2))
+end
+function Base.:&(trunc1::TruncationStrategy, trunc2::TruncationIntersection)
+    return TruncationIntersection((trunc1, trunc2.components...))
+end
+
 # truncate!
 # ---------
 # Generic implementation: `findtruncated` followed by indexing
@@ -147,6 +176,11 @@ function findtruncated(values::AbstractVector, strategy::TruncationKeepAbove)
     return 1:i
 end
 
+function findtruncated(values::AbstractVector, strategy::TruncationIntersection)
+    inds = map(Base.Fix1(findtruncated, values), strategy.components)
+    return intersect(inds...)
+end
+
 """
     TruncatedAlgorithm(alg::AbstractAlgorithm, trunc::TruncationAlgorithm)
 
diff --git a/test/runtests.jl b/test/runtests.jl
index 541c7da8..7ad7c216 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -1,5 +1,8 @@
 using SafeTestsets
 
+@safetestset "Truncate" begin
+    include("truncate.jl")
+end
 @safetestset "QR / LQ Decomposition" begin
     include("qr.jl")
     include("lq.jl")
diff --git a/test/svd.jl b/test/svd.jl
index b92c2e45..e40a69e9 100644
--- a/test/svd.jl
+++ b/test/svd.jl
@@ -3,7 +3,7 @@ using Test
 using TestExtras
 using StableRNGs
 using LinearAlgebra: LinearAlgebra, Diagonal, I, isposdef
-using MatrixAlgebraKit: diagview
+using MatrixAlgebraKit: TruncationKeepAbove, diagview
 
 @testset "svd_compact! for T = $T" for T in (Float32, Float64, ComplexF32, ComplexF64)
     rng = StableRNG(123)
@@ -115,3 +115,33 @@ end
         end
     end
 end
+
+@testset "svd_trunc! mix maxrank and tol for T = $T" for T in
+                                                         (Float32, Float64, ComplexF32,
+                                                          ComplexF64)
+    rng = StableRNG(123)
+    if LinearAlgebra.LAPACK.version() < v"3.12.0"
+        algs = (LAPACK_DivideAndConquer(), LAPACK_QRIteration(), LAPACK_Bisection())
+    else
+        algs = (LAPACK_DivideAndConquer(), LAPACK_QRIteration(), LAPACK_Bisection(),
+                LAPACK_Jacobi())
+    end
+    m = 4
+    @testset "algorithm $alg" for alg in algs
+        U = qr_compact(randn(rng, T, m, m))[1]
+        S = Diagonal([0.9, 0.3, 0.1, 0.01])
+        Vᴴ = qr_compact(randn(rng, T, m, m))[1]
+        A = U * S * Vᴴ
+
+        for trunc_fun in ((rtol, maxrank) -> (; rtol, maxrank),
+                          (rtol, maxrank) -> truncrank(maxrank) & TruncationKeepAbove(0, rtol))
+            U1, S1, V1ᴴ = svd_trunc(A; alg, trunc=trunc_fun(0.2, 1))
+            @test length(S1.diag) == 1
+            @test S1.diag ≈ S.diag[1:1] rtol = sqrt(eps(real(T)))
+
+            U2, S2, V2ᴴ = svd_trunc(A; alg, trunc=trunc_fun(0.2, 3))
+            @test length(S2.diag) == 2
+            @test S2.diag ≈ S.diag[1:2] rtol = sqrt(eps(real(T)))
+        end
+    end
+end
diff --git a/test/truncate.jl b/test/truncate.jl
new file mode 100644
index 00000000..5004a39d
--- /dev/null
+++ b/test/truncate.jl
@@ -0,0 +1,29 @@
+using MatrixAlgebraKit
+using Test
+using TestExtras
+using MatrixAlgebraKit: NoTruncation, TruncationIntersection, TruncationKeepAbove,
+                        TruncationStrategy
+
+@testset "truncate" begin
+    trunc = @constinferred TruncationStrategy()
+    @test trunc isa NoTruncation
+
+    trunc = @constinferred TruncationStrategy(; atol=1e-2, rtol=1e-3)
+    @test trunc isa TruncationKeepAbove
+    @test trunc == TruncationKeepAbove(1e-2, 1e-3)
+    @test trunc.atol == 1e-2
+    @test trunc.rtol == 1e-3
+
+    trunc = @constinferred TruncationStrategy(; maxrank=10)
+    @test trunc isa TruncationKeepSorted
+    @test trunc == truncrank(10)
+    @test trunc.howmany == 10
+    @test trunc.sortby == abs
+    @test trunc.rev == true
+
+    trunc = @constinferred TruncationStrategy(; atol=1e-2, rtol=1e-3, maxrank=10)
+    @test trunc isa TruncationIntersection
+    @test trunc == truncrank(10) & TruncationKeepAbove(1e-2, 1e-3)
+    @test trunc.components[1] == truncrank(10)
+    @test trunc.components[2] == TruncationKeepAbove(1e-2, 1e-3)
+end