diff --git a/src/CPU.jl b/src/CPU.jl
index 4df7e01..892acc5 100644
--- a/src/CPU.jl
+++ b/src/CPU.jl
@@ -324,7 +324,8 @@ function bidiag_forward!(u::Vector{T}, g::FixedEffectCoefficients, fem::FixedEff
 		# serial: everything in one pass, gathers accumulated directly into g
 		s = _bidiag_chunk!(u, gs, blocks, qrowss, vs, T(c), eachindex(u))
 	end
-	return T(sqrt(s))
+	# The asserted norm type prevents boxing in LSMR's scalar recurrences.
+	return T(sqrt(s))::T
 end
 
 # u[i] ← c * u[i] + Σ_blocks fit_i; accumulates each block's gather into
diff --git a/test/solve.jl b/test/solve.jl
index ac70586..8738bc9 100644
--- a/test/solve.jl
+++ b/test/solve.jl
@@ -21,6 +21,16 @@ r_ols =  [-0.2015993617092453,  0.2015993617092464, -0.2015993617092463,  0.2015
 @test iterz == 0
 @test all(iszero, rz)
 
+@testset "Inferred bidiagonalization norm" begin
+	for T in (Float32, Float64)
+		solver = FixedEffects.AbstractFixedEffectSolver{T}(fes, uweights(T, length(x)), Val{:cpu})
+		u = T.(x)
+		fill!(solver.v, one(T))
+		@test (@inferred FixedEffects.bidiag_forward!(
+			u, solver.g, solver.m, solver.v, zero(T))) isa T
+	end
+end
+
 @testset "maxiter semantics" begin
 	(r0, iter0, conv0) = @test_logs (:warn, r"solve_residuals!") solve_residuals!(deepcopy(x), fes; maxiter = 0)
 	@test iter0 == 0