diff --git a/Project.toml b/Project.toml
index c814f6a..429a984 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "OrdinaryDiffEqOperatorSplitting"
 uuid = "760fc936-9fa0-4281-9c1a-468957eedc89"
-version = "0.4.3"
+version = "0.4.4"
 authors = ["Dennis Ogiermann <termi-official@users.noreply.github.com> and contributors"]
 
 [deps]
diff --git a/src/OrdinaryDiffEqOperatorSplitting.jl b/src/OrdinaryDiffEqOperatorSplitting.jl
index 773e179..878d400 100644
--- a/src/OrdinaryDiffEqOperatorSplitting.jl
+++ b/src/OrdinaryDiffEqOperatorSplitting.jl
@@ -146,6 +146,16 @@ end
 _inner_verbose(verbose) = verbose
 _process_verbose(verbose) = verbose
 
+"""
+    inner_verbosity(verbose)
+
+The verbosity a leaf integrator under a splitting node runs with: the `inner_verbosity`
+of an [`OperatorSplittingVerbosity`](@ref), or `verbose` itself where it already is a
+leaf setting. A leaf integrator built from `config.values.verbose` passes it through
+here; the splitting toggles live on the node, not on its leaves.
+"""
+inner_verbosity(verbose) = _inner_verbose(verbose)
+
 # `verbose` reaches us either as a Bool or, through DiffEqBase v7's `init`, as a
 # verbosity specifier whose first type parameter is the on/off flag. Neither can be
 # used in a boolean context directly.
diff --git a/src/config_tree.jl b/src/config_tree.jl
index 2d53472..26513c3 100644
--- a/src/config_tree.jl
+++ b/src/config_tree.jl
@@ -429,9 +429,17 @@ const SPLIT_OPTION_KEYS = (
 function split_integrator_options(values::NamedTuple)
     inner = inner_values(values)
     known = filter(in(SPLIT_OPTION_KEYS), keys(inner))
-    return IntegratorOptions(;
-        verbose = values.verbose,
-        adaptive = values.adaptive,
-        NamedTuple{known}(inner)...
+    opts = NamedTuple{known}(inner)
+    # `dtmin` and `dtmax` share the node's time type: a `Float32` time span with the
+    # default `dtmin` would otherwise leave the two with no common type parameter.
+    T = typeof(values.dt)
+    opts = merge(
+        opts, (;
+            dtmin = T(get(opts, :dtmin, default_dtmin(T))),
+            dtmax = T(get(opts, :dtmax, typemax(T))),
+        )
     )
+    return IntegratorOptions(; verbose = values.verbose, adaptive = values.adaptive, opts...)
 end
+default_dtmin(::Type{T}) where {T <: AbstractFloat} = eps(T)
+default_dtmin(::Type{T}) where {T} = zero(T)
diff --git a/src/integrator.jl b/src/integrator.jl
index 7663e84..d4b20e4 100644
--- a/src/integrator.jl
+++ b/src/integrator.jl
@@ -8,8 +8,8 @@ IntegratorStats() = IntegratorStats(0, 0)
 
 Base.@kwdef mutable struct IntegratorOptions{tType, fType, vbType, F3, atolType, rtolType, normType}
     adaptive::Bool
-    dtmin::tType = eps(Float64)
-    dtmax::tType = Inf
+    dtmin::tType
+    dtmax::tType
     failfactor::fType = 4.0
     verbose::vbType = DEFAULT_VERBOSITY
     isoutofdomain::F3 = DiffEqBase.ODE_DEFAULT_ISOUTOFDOMAIN
diff --git a/test/precision.jl b/test/precision.jl
new file mode 100644
index 0000000..830708b
--- /dev/null
+++ b/test/precision.jl
@@ -0,0 +1,28 @@
+using OrdinaryDiffEqLowOrderRK
+using OrdinaryDiffEqOperatorSplitting
+using Test
+
+@testset "Float32 time span" begin
+    f(du, u, p, t) = @. du = -u
+    split_f = GenericSplitFunction((ODEFunction(f),), (1:1,))
+    prob = OperatorSplittingProblem(split_f, Float32[1.0], (0.0f0, 1.0f0))
+    alg = LieTrotterGodunov((Euler(),))
+
+    integrator = init(prob, alg; dt = 0.1f0)
+    @test integrator.opts.dtmin === eps(Float32)
+    @test integrator.opts.dtmax === 1.0f0
+    step!(integrator)
+    @test integrator.t === 0.1f0
+    @test integrator.u ≈ Float32[0.9]
+
+    # An explicitly given bound is converted to the time type.
+    integrator = init(prob, alg; dt = 0.1f0, dtmin = 1.0e-3)
+    @test integrator.opts.dtmin === 1.0f-3
+end
+
+@testset "inner_verbosity" begin
+    @test OrdinaryDiffEqOperatorSplitting.inner_verbosity(true) isa OrdinaryDiffEqOperatorSplitting.DiffEqBase.DEVerbosity
+    v = OrdinaryDiffEqOperatorSplitting.OperatorSplittingVerbosity(OrdinaryDiffEqOperatorSplitting.SciMLLogging.Standard())
+    @test OrdinaryDiffEqOperatorSplitting.inner_verbosity(v) === v.inner_verbosity
+    @test OrdinaryDiffEqOperatorSplitting.inner_verbosity(v.inner_verbosity) === v.inner_verbosity
+end