diff --git a/src/ParallelKernel/parallel.jl b/src/ParallelKernel/parallel.jl
index f8dae83..742f7e5 100644
--- a/src/ParallelKernel/parallel.jl
+++ b/src/ParallelKernel/parallel.jl
@@ -485,7 +485,7 @@ function handle_inverses(body::Expr)
 end
 
 function handle_padding(caller::Module, body::Expr, padding::Bool, indices; handle_view_accesses::Bool=true, handle_indexing::Bool=true, dir_handling::Bool=true, delay_dir_handling::Bool=false)
-    if (handle_indexing) 
+    if (handle_indexing)
         body = substitute_indices_inn(body, padding)
         if (dir_handling) body = substitute_indices_dir(caller, body, padding; delay_handling=delay_dir_handling) end
         body = substitute_firstlastindex(caller, body, padding)
@@ -519,7 +519,7 @@ function substitute_indices_dir(caller::Module, expr::Expr, padding::Bool; delay
                         if @capture(ex, A_[indices_expr__]) && any(map(inexpr_walk, indices_expr, INDICES_DIR))
                             A_parent = promote_to_parent(A)
                             ex = substitute(ex, NamedTuple{INDICES_DIR}(
-                                ((A_parent==B_parent) ? ix : :($ix - (size($B_parent, 1) > size($A_parent, 1))), 
+                                ((A_parent==B_parent) ? ix : :($ix - (size($B_parent, 1) > size($A_parent, 1))),
                                  (A_parent==B_parent) ? iy : :($iy - (size($B_parent, 2) > size($A_parent, 2))),
                                  (A_parent==B_parent) ? iz : :($iz - (size($B_parent, 3) > size($A_parent, 3))))
                                 ); inQuoteNode=true)
@@ -558,7 +558,7 @@ end
 
 function substitute_firstlastindex(caller::Module, body::Expr, padding::Bool)
     return postwalk(body) do ex
-        if @capture(ex, f_(args__)) 
+        if @capture(ex, f_(args__))
             if     (f == :firstindex) return _firstindex(caller, args..., padding)
             elseif (f == :lastindex)  return _lastindex(caller, args..., padding)
             else return ex
@@ -804,9 +804,9 @@ end
 
 function compute_nthreads(maxsize; nthreads_x_max=NTHREADS_X_MAX, nthreads_max=NTHREADS_MAX, flatdim=0) # This is a heuristic, which results in (32,8,1) threads, except if maxsize[1] < 32 or maxsize[2] < 8.
     maxsize = promote_maxsize(maxsize)
-    nthreads_x = min(nthreads_x_max,                                 (flatdim==1) ? 1 : maxsize[1])
-    nthreads_y = min(ceil(Int,nthreads_max/nthreads_x),              (flatdim==2) ? 1 : maxsize[2])
-    nthreads_z = min(ceil(Int,nthreads_max/(nthreads_x*nthreads_y)), (flatdim==3) ? 1 : maxsize[3])
+    nthreads_x = min(nthreads_x_max,                                                (flatdim==1) ? 1 : maxsize[1])
+    nthreads_y = min(max(floor(Int,nthreads_max/nthreads_x), 1),                    (flatdim==2) ? 1 : maxsize[2])
+    nthreads_z = min(max(floor(Int,nthreads_max/(nthreads_x*nthreads_y)), 1),       (flatdim==3) ? 1 : maxsize[3]) # NOTE: the thread budget of each dimension is rounded down, because rounding it up can make the total number of threads exceed nthreads_max whenever a previous dimension was clamped to a smaller maxsize.
     return (nthreads_x, nthreads_y , nthreads_z)
 end
 
@@ -892,7 +892,7 @@ function create_gpu_or_xpu_call(package::Symbol, nblocks::Union{Symbol,Expr}, nt
             else                           @ModuleInternalError("unsupported GPU package (obtained: $package).")
             end
             if !isnothing(shmem_expr)
-                backend_kwargs_expr = (backend_kwargs_expr..., shmem_expr) 
+                backend_kwargs_expr = (backend_kwargs_expr..., shmem_expr)
             end
         end
         if     (package == PKG_CUDA)   return :( CUDA.@cuda blocks=$nblocks threads=$nthreads stream=$stream $(backend_kwargs_expr...) $kernelcall; $synccall )
@@ -933,4 +933,4 @@ function default_stream(package)
     elseif (package == PKG_KERNELABSTRACTIONS) return :(nothing)
     else                            @ModuleInternalError("unsupported GPU package (obtained: $package).")
     end
-end
\ No newline at end of file
+end
diff --git a/test/ParallelKernel/test_parallel.jl b/test/ParallelKernel/test_parallel.jl
index 5358b6e..a8a53bd 100644
--- a/test/ParallelKernel/test_parallel.jl
+++ b/test/ParallelKernel/test_parallel.jl
@@ -5,7 +5,7 @@ using ParallelStencil.ParallelKernel
 import ParallelStencil.ParallelKernel.AD
 import ParallelStencil.ParallelKernel: @reset_parallel_kernel, @is_initialized, SUPPORTED_PACKAGES, PKG_CUDA, PKG_AMDGPU, PKG_METAL, PKG_THREADS, PKG_POLYESTER, PKG_KERNELABSTRACTIONS, INDICES, ARRAYTYPES, FIELDTYPES, SCALARTYPES
 import ParallelStencil.ParallelKernel: @require, @prettystring, @gorgeousstring, @isgpu, @iscpu, interpolate, @select_hardware, @current_hardware, handle
-import ParallelStencil.ParallelKernel: checkargs_parallel, checkargs_parallel_indices, parallel_indices, maxsize
+import ParallelStencil.ParallelKernel: checkargs_parallel, checkargs_parallel_indices, parallel_indices, maxsize, compute_nthreads, NTHREADS_X_MAX_AMDGPU, NTHREADS_MAX
 using ParallelStencil.ParallelKernel.Exceptions
 TEST_PACKAGES = SUPPORTED_PACKAGES
 @static if PKG_CUDA in TEST_PACKAGES
@@ -219,6 +219,24 @@ eval(:(
                     @test maxsize((x=8, y=[9 9; 9 9; 9 9]), [7 7 7; 7 7 7]) == (3, 3, 1)
                     @test maxsize(BitstypeStruct(5, 6.0), 8, (x=[9 9; 9 9; 9 9], y=[9 9; 9 9; 9 9]), (x=[7 7 7; 7 7 7], y=[7 7 7; 7 7 7])) == (3, 3, 1)
                 end;
+                @testset "compute_nthreads" begin
+                    @test compute_nthreads(256)                                          == (32, 1, 1)
+                    @test compute_nthreads((256, 256))                                   == (32, 8, 1)
+                    @test compute_nthreads((256, 256, 256))                              == (32, 8, 1)
+                    @test compute_nthreads((256, 256, 256); nthreads_x_max=NTHREADS_X_MAX_AMDGPU) == (64, 4, 1)
+                    @test compute_nthreads((8, 8, 8))                                    == (8, 8, 4)
+                    @test compute_nthreads((256, 256, 256); nthreads_max=128, flatdim=3) == (32, 4, 1)
+                    @testset "nthreads never exceeds nthreads_max" begin # NOTE: rounding the thread budget of each dimension up used to make the total number of threads exceed nthreads_max whenever a previous dimension was clamped to a smaller maxsize, resulting in a launch failure (e.g. maxsize=(256,5,128) resulted in (32,5,2)=320 threads).
+                        @test compute_nthreads((256, 5, 128)) == (32, 5, 1)
+                        @test compute_nthreads((256, 3, 128)) == (32, 3, 2)
+                        @test compute_nthreads((10, 100, 100)) == (10, 25, 1)
+                        maxsizes = ((i, j, k) for i in 1:70, j in 1:70, k in 1:70) # NOTE: `ms` is used below instead of `maxsize` in order not to shadow the imported function `maxsize`.
+                        @test all(prod(compute_nthreads(ms)) <= NTHREADS_MAX for ms in maxsizes)
+                        @test all(prod(compute_nthreads(ms; nthreads_x_max=NTHREADS_X_MAX_AMDGPU)) <= NTHREADS_MAX for ms in maxsizes)
+                        @test all(prod(compute_nthreads(ms; nthreads_max=128, flatdim=loopdim)) <= 128 for ms in maxsizes, loopdim in 1:3)
+                        @test all(all(compute_nthreads(ms) .>= 1) for ms in maxsizes)
+                    end;
+                end;
             end;
             @static if $package != $PKG_POLYESTER # Enzyme does not support Polyester.
                 @testset "@parallel ∇" begin