diff --git a/src/factorizations/truncation.jl b/src/factorizations/truncation.jl
index e8e113ec1..ff9c8a2e6 100644
--- a/src/factorizations/truncation.jl
+++ b/src/factorizations/truncation.jl
@@ -171,7 +171,8 @@ function MAK.findtruncated(values::SectorVector, strategy::TruncationByOrder)
 
     # dimensions are all 1 so no need to account for weight
     if FusionStyle(I) isa UniqueFusion
-        perm = partialsortperm(parent(values), 1:strategy.howmany; strategy.by, strategy.rev)
+        howmany = min(length(parent(values)), strategy.howmany)
+        perm = partialsortperm(parent(values), 1:howmany; strategy.by, strategy.rev)
         result = similar(values, Bool)
         fill!(parent(result), false)
         parent(result)[perm] .= true
diff --git a/test/tensors/factorizations.jl b/test/tensors/factorizations.jl
index 7e6510b6c..48dfaf6f1 100644
--- a/test/tensors/factorizations.jl
+++ b/test/tensors/factorizations.jl
@@ -254,6 +254,14 @@ for V in spacelist
                 @test isisometric(U)
                 @test isisometric(Vᴴ; side = :right)
 
+                # when rank of t is already smaller than truncrank
+                t_rank = ceil(Int, min(dim(codomain(t)), dim(domain(t))))
+                U, S, Vᴴ, ϵ = @constinferred svd_trunc(t; trunc = truncrank(t_rank + 1))
+                @test U * S * Vᴴ ≈ t
+                @test ϵ ≈ 0
+                @test isisometric(U)
+                @test isisometric(Vᴴ; side = :right)
+
                 # dimension of S is a float for IsingBimodule
                 nvals = round(Int, dim(domain(S)) / 2)
                 trunc = truncrank(nvals)