diff --git a/src/OhMyThreads.jl b/src/OhMyThreads.jl
index 7db5788b..473d65b1 100644
--- a/src/OhMyThreads.jl
+++ b/src/OhMyThreads.jl
@@ -38,6 +38,7 @@ This data is divided into chunks to be worked on in parallel using [ChunkSplitte
 - `schedule::Symbol` (default `:dynamic`), determines how the parallel portions of the calculation are scheduled. Options are one of
     - `:dynamic`: generally preferred since it is more flexible and better at load balancing, and won't interfere with other multithreaded functions which may be running on the system.
     - `:static`: can sometimes be more performant than `:dynamic` when the time it takes to complete a step of the calculation is highly uniform, and no other parallel functions are running at the same time.
+    - `:greedy`: best option for load-balancing slower, uneven computations, but does carry some additional overhead. This schedule will read from the contents of `A` in a non-deterministic order, and thus your reducing `op` **must** be [commutative](https://en.wikipedia.org/wiki/Commutative_property) in addition to being associative, or you could get incorrect results! This schedule will however work with non-`AbstractArray` iterables. If you use the `:greedy` scheduler, we strongly recommend you provide an `init` keyword argument.
     - `:interactive`: like `:dynamic` but runs on the high-priority interactive threadpool. This should be used very carefully since tasks on this threadpool should not be allowed to run for a long time without `yield`ing as it can interfere with [heartbeat](https://en.wikipedia.org/wiki/Heartbeat_(computing)) processes running on the interactive threadpool.
 - `outputtype::Type` (default `Any`) will work as the asserted output type of parallel calculations. This is typically only
 needed if you are using a `:static` schedule, since the `:dynamic` schedule is uses [StableTasks.jl](https://github.com/MasonProtter/StableTasks.jl), but if you experience problems with type stability, you may be able to recover it with the `outputtype` keyword argument.
@@ -77,6 +78,7 @@ This data is divided into chunks to be worked on in parallel using [ChunkSplitte
 - `schedule::Symbol` (default `:dynamic`), determines how the parallel portions of the calculation are scheduled. Options are one of
     - `:dynamic`: generally preferred since it is more flexible and better at load balancing, and won't interfere with other multithreaded functions which may be running on the system.
     - `:static`: can sometimes be more performant than `:dynamic` when the time it takes to complete a step of the calculation is highly uniform, and no other parallel functions are running at the same time.
+    - `:greedy`: best option for load-balancing slower, uneven computations, but does carry some additional overhead. This schedule will read from the contents of `A` in a non-deterministic order, and thus your reducing `op` **must** be [commutative](https://en.wikipedia.org/wiki/Commutative_property) in addition to being associative, or you could get incorrect results! This schedule will however work with non-`AbstractArray` iterables. If you use the `:greedy` scheduler, we strongly recommend you provide an `init` keyword argument.
     - `:interactive`: like `:dynamic` but runs on the high-priority interactive threadpool. This should be used very carefully since tasks on this threadpool should not be allowed to run for a long time without `yield`ing as it can interfere with [heartbeat](https://en.wikipedia.org/wiki/Heartbeat_(computing)) processes running on the interactive threadpool.
 - `outputtype::Type` (default `Any`) will work as the asserted output type of parallel calculations. This is typically only
 needed if you are using a `:static` schedule, since the `:dynamic` schedule is uses [StableTasks.jl](https://github.com/MasonProtter/StableTasks.jl), but if you experience problems with type stability, you may be able to recover it with the `outputtype` keyword argument.
@@ -117,6 +119,7 @@ This data is divided into chunks to be worked on in parallel using [ChunkSplitte
 - `schedule::Symbol` (default `:dynamic`), determines how the parallel portions of the calculation are scheduled. Options are one of
     - `:dynamic`: generally preferred since it is more flexible and better at load balancing, and won't interfere with other multithreaded functions which may be running on the system.
     - `:static`: can sometimes be more performant than `:dynamic` when the time it takes to complete a step of the calculation is highly uniform, and no other parallel functions are running at the same time.
+    - `:greedy`: best option for load-balancing slower, uneven computations, but does carry some additional overhead. This schedule will read from the contents of `A` in a non-deterministic order, and thus your reducing `op` **must** be [commutative](https://en.wikipedia.org/wiki/Commutative_property) in addition to being associative, or you could get incorrect results! This schedule will however work with non-`AbstractArray` iterables. If you use the `:greedy` scheduler, we strongly recommend you provide an `init` keyword argument.
     - `:interactive`: like `:dynamic` but runs on the high-priority interactive threadpool. This should be used very carefully since tasks on this threadpool should not be allowed to run for a long time without `yield`ing as it can interfere with [heartbeat](https://en.wikipedia.org/wiki/Heartbeat_(computing)) processes running on the interactive threadpool.
 - `outputtype::Type` (default `Any`) will work as the asserted output type of parallel calculations. This is typically only
 needed if you are using a `:static` schedule, since the `:dynamic` schedule is uses [StableTasks.jl](https://github.com/MasonProtter/StableTasks.jl), but if you experience problems with type stability, you may be able to recover it with the `outputtype` keyword argument.
@@ -142,6 +145,7 @@ A multithreaded function like `Base.foreach`. Apply `f` to each element of `A` o
 - `schedule::Symbol` (default `:dynamic`), determines how the parallel portions of the calculation are scheduled. Options are one of
     - `:dynamic`: generally preferred since it is more flexible and better at load balancing, and won't interfere with other multithreaded functions which may be running on the system.
     - `:static`: can sometimes be more performant than `:dynamic` when the time it takes to complete a step of the calculation is highly uniform, and no other parallel functions are running at the same time.
+    - `:greedy`: best option for load-balancing slower, uneven computations, but does carry some additional overhead.
     - `:interactive`: like `:dynamic` but runs on the high-priority interactive threadpool. This should be used very carefully since tasks on this threadpool should not be allowed to run for a long time without `yield`ing as it can interfere with [heartbeat](https://en.wikipedia.org/wiki/Heartbeat_(computing)) processes running on the interactive threadpool.
 """
 function tforeach end
@@ -165,6 +169,7 @@ fewer allocations than the version where `OutputElementType` is not specified.
 - `schedule::Symbol` (default `:dynamic`), determines how the parallel portions of the calculation are scheduled. Options are one of
     - `:dynamic`: generally preferred since it is more flexible and better at load balancing, and won't interfere with other multithreaded functions which may be running on the system.
     - `:static`: can sometimes be more performant than `:dynamic` when the time it takes to complete a step of the calculation is highly uniform, and no other parallel functions are running at the same time.
+    - `:greedy`: best option for load-balancing slower, uneven computations, but does carry some additional overhead. This schedule only works if the `OutputElementType` argument is provided.
     - `:interactive`: like `:dynamic` but runs on the high-priority interactive threadpool. This should be used very carefully since tasks on this threadpool should not be allowed to run for a long time without `yield`ing as it can interfere with [heartbeat](https://en.wikipedia.org/wiki/Heartbeat_(computing)) processes running on the interactive threadpool.
 """
 function tmap end
@@ -185,6 +190,7 @@ of `out[i] = f(A[i])` for each index `i` of `A` and `out`.
 - `schedule::Symbol` (default `:dynamic`), determines how the parallel portions of the calculation are scheduled. Options are one of
     - `:dynamic`: generally preferred since it is more flexible and better at load balancing, and won't interfere with other multithreaded functions which may be running on the system.
     - `:static`: can sometimes be more performant than `:dynamic` when the time it takes to complete a step of the calculation is highly uniform, and no other parallel functions are running at the same time.
+    - `:greedy`: best option for load-balancing slower, uneven computations, but does carry some additional overhead.
     - `:interactive`: like `:dynamic` but runs on the high-priority interactive threadpool. This should be used very carefully since tasks on this threadpool should not be allowed to run for a long time without `yield`ing as it can interfere with [heartbeat](https://en.wikipedia.org/wiki/Heartbeat_(computing)) processes running on the interactive threadpool.
 """
 function tmap! end
@@ -203,6 +209,7 @@ inputs. The optional argument `OutputElementType` will select a specific element
 - `schedule::Symbol` (default `:dynamic`), determines how the parallel portions of the calculation are scheduled. Options are one of
     - `:dynamic`: generally preferred since it is more flexible and better at load balancing, and won't interfere with other multithreaded functions which may be running on the system.
     - `:static`: can sometimes be more performant than `:dynamic` when the time it takes to complete a step of the calculation is highly uniform, and no other parallel functions are running at the same time.
+    - `:greedy`: best option for load-balancing slower, uneven computations, but does carry some additional overhead. This schedule only works if the `OutputElementType` argument is provided.
     - `:interactive`: like `:dynamic` but runs on the high-priority interactive threadpool. This should be used very carefully since tasks on this threadpool should not be allowed to run for a long time without `yield`ing as it can interfere with [heartbeat](https://en.wikipedia.org/wiki/Heartbeat_(computing)) processes running on the interactive threadpool.
 """
 function tcollect end
diff --git a/src/implementation.jl b/src/implementation.jl
index a2a6ee0c..69846c52 100644
--- a/src/implementation.jl
+++ b/src/implementation.jl
@@ -14,41 +14,60 @@ function tmapreduce(f, op, Arrs...;
     split::Symbol=:batch,
     schedule::Symbol=:dynamic,
     outputtype::Type=Any,
-    kwargs...)
+    mapreduce_kwargs...)
     if schedule === :dynamic 
-        _tmapreduce(f, op, Arrs, outputtype, nchunks, split, :default; kwargs...)
-    elseif schedule === :interactive 
-        _tmapreduce(f, op, Arrs, outputtype, nchunks, split, :interactive; kwargs...)
+        _tmapreduce(f, op, Arrs, outputtype, nchunks, split, :default, mapreduce_kwargs)
+    elseif schedule === :interactive
+        _tmapreduce(f, op, Arrs, outputtype, nchunks, split, :interactive, mapreduce_kwargs)
+    elseif schedule === :greedy
+        _tmapreduce_greedy(f, op, Arrs, outputtype, nchunks, split, mapreduce_kwargs)
     elseif schedule === :static
-        _tmapreduce_static(f, op, Arrs, outputtype, nchunks, split; kwargs...)
+        _tmapreduce_static(f, op, Arrs, outputtype, nchunks, split, mapreduce_kwargs)
     else
         schedule_err(schedule)
     end
 end
-@noinline schedule_err(s) = error(ArgumentError("Invalid schedule option: $s, expected :dynamic or :static."))
+@noinline schedule_err(s) = error(ArgumentError("Invalid schedule option: $s, expected :dynamic, :interactive, :greedy, or :static."))
 
 treducemap(op, f, A...; kwargs...) = tmapreduce(f, op, A...; kwargs...)
 
-function _tmapreduce(f, op, Arrs, ::Type{OutputType}, nchunks, split, schedule; kwargs...)::OutputType where {OutputType}
+function _tmapreduce(f, op, Arrs, ::Type{OutputType}, nchunks, split, threadpool, mapreduce_kwargs)::OutputType where {OutputType}
     check_all_have_same_indices(Arrs)
     tasks = map(chunks(first(Arrs); n=nchunks, split)) do inds
         args = map(A -> A[inds], Arrs)
-        @spawn schedule mapreduce(f, op, args...; kwargs...)
+        @spawn threadpool mapreduce(f, op, args...; $mapreduce_kwargs...)
     end
     mapreduce(fetch, op, tasks)
 end
 
-function _tmapreduce_static(f, op, Arrs, ::Type{OutputType}, nchunks, split; kwargs...) where {OutputType}
-    nt = nthreads()
-    check_all_have_same_indices(Arrs)
-    if nchunks > nt
-        # We could implement strategies, like round-robin, in the future
-        throw(ArgumentError("We currently only support `nchunks <= nthreads()` for static scheduling."))
+function _tmapreduce_greedy(f, op, Arrs, ::Type{OutputType}, nchunks, split, mapreduce_kwargs)::OutputType where {OutputType}
+    if Base.IteratorSize(first(Arrs)) isa Base.SizeUnknown
+        ntasks = nchunks
+    else
+        check_all_have_same_indices(Arrs)
+        nchunks > 0 || throw("Error: nchunks must be a positive integer")
+    end
+    ch = Channel{Tuple{eltype.(Arrs)...}}(0; spawn=true) do ch
+        for args ∈ zip(Arrs...)
+            put!(ch, args)
+        end
+    end
+    tasks = map(1:ntasks) do _
+        @spawn mapreduce(op, ch; mapreduce_kwargs...) do args
+            f(args...)
+        end
     end
-    tasks = map(enumerate(chunks(first(Arrs); n=nchunks, split))) do (c, inds)
+    mapreduce(fetch, op, tasks; mapreduce_kwargs...)
+end
+
+function _tmapreduce_static(f, op, Arrs, ::Type{OutputType}, nchunks, split, mapreduce_kwargs) where {OutputType}
+    check_all_have_same_indices(Arrs)
+    nchunks > 0 || throw("Error: nchunks must be a positive integer")
+    n = min(nthreads(), nchunks) # We could implement strategies, like round-robin, in the future
+    tasks = map(enumerate(chunks(first(Arrs); n, split))) do (c, inds)
         tid = @inbounds nthtid(c)
         args = map(A -> A[inds], Arrs)
-        @spawnat tid mapreduce(f, op, args...; kwargs...)
+        @spawnat tid mapreduce(f, op, args...; mapreduce_kwargs...)
     end
     mapreduce(fetch, op, tasks)
 end
@@ -79,10 +98,13 @@ function tmap(f, ::Type{T}, A::AbstractArray, _Arrs::AbstractArray...; kwargs...
     tmap!(f, similar(A, T), Arrs...; kwargs...)
 end
 
-function tmap(f, A::AbstractArray, _Arrs::AbstractArray...; nchunks::Int=nthreads(), kwargs...)
+function tmap(f, A::AbstractArray, _Arrs::AbstractArray...; nchunks::Int=nthreads(), schedule=:dynamic, kwargs...)
     Arrs = (A, _Arrs...)
     check_all_have_same_indices(Arrs)
     the_chunks = collect(chunks(A; n=nchunks))
+    if schedule == :greedy
+        error("Greedy schedules are not supported with `tmap` unless you provide an `OutputElementType` argument, since the greedy schedule requires a commutative reducing operator.")
+    end
     # It's vital that we force split=:batch here because we're not doing a commutative operation!
     v = tmapreduce(append!!, the_chunks; kwargs...,  nchunks, split=:batch) do inds
         args = map(A -> @view(A[inds]), Arrs)
diff --git a/test/runtests.jl b/test/runtests.jl
index f82c2140..244e11c1 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -1,43 +1,48 @@
 using Test, OhMyThreads
 
-@testset "Basics" begin
-    for (~, f, op, itrs) ∈ [
-        (isapprox, sin∘*, +, (rand(ComplexF64, 10, 10), rand(-10:10, 10, 10))),
-        (isapprox, cos, max, (1:100000,)),
-        (==, round, vcat, (randn(1000),)),
-        (==, last, *, ([1=>"a", 2=>"b", 3=>"c", 4=>"d", 5=>"e"],))
-    ]
-        @testset for schedule ∈ (:static, :dynamic, :interactive)
-            @testset for split ∈ (:batch, :scatter)
-                if split == :scatter # scatter only works for commutative operators
-                    if op ∈ (vcat, *)
-                        continue
-                    end
-                end
-                for nchunks ∈ (1, 2, 6, 10)
-                    if schedule == :static && nchunks > Threads.nthreads()
-                        continue
-                    end
-                    kwargs = (; schedule, split, nchunks)
-                    mapreduce_f_op_itr = mapreduce(f, op, itrs...)
-                    @test tmapreduce(f, op, itrs...; kwargs...) ~ mapreduce_f_op_itr
-                    @test treducemap(op, f, itrs...; kwargs...) ~ mapreduce_f_op_itr
-                    @test treduce(op, f.(itrs...); kwargs...) ~ mapreduce_f_op_itr
+sets_to_test = [
+    (~=isapprox, f=sin∘*, op=+, itrs = (rand(ComplexF64, 10, 10), rand(-10:10, 10, 10)), init=complex(0.0))
+    (~=isapprox, f=cos, op=max, itrs = (1:100000,), init=0.0)
+    (~=(==), f=round, op=vcat, itrs = (randn(1000),), init=Float64[])
+    (~=(==), f=last, op=*, itrs = ([1=>"a", 2=>"b", 3=>"c", 4=>"d", 5=>"e"],), init="")
+]
 
-                    map_f_itr = map(f, itrs...)
-                    @test all(tmap(f, Any, itrs...; kwargs...) .~ map_f_itr)
-                    @test all(tcollect(Any, (f(x...) for x in collect(zip(itrs...))); kwargs...) .~ map_f_itr)
-                    @test all(tcollect(Any, f.(itrs...); kwargs...) .~ map_f_itr)
 
-                    @test tmap(f, itrs...; kwargs...) ~ map_f_itr
-                    @test tcollect((f(x...) for x in collect(zip(itrs...))); kwargs...) ~ map_f_itr
-                    @test tcollect(f.(itrs...); kwargs...) ~ map_f_itr
-                    
-                    RT = Core.Compiler.return_type(f, Tuple{eltype.(itrs)...})
-                    
-                    @test tmap(f, RT, itrs...; kwargs...) ~ map_f_itr
-                    @test tcollect(RT, (f(x...) for x in collect(zip(itrs...))); kwargs...) ~ map_f_itr
-                    @test tcollect(RT, f.(itrs...); kwargs...) ~ map_f_itr
+@testset "Basics" begin
+    for (; ~, f, op, itrs, init) ∈ sets_to_test
+        @testset "f=$f, op=$op, itrs::$(typeof(itrs))" begin
+            @testset for schedule ∈ (:static, :dynamic, :interactive, :greedy)
+                @testset for split ∈ (:batch, :scatter)
+                    for nchunks ∈ (1, 2, 6)
+                        rand() < 0.25 && continue # we don't really want full coverage here
+                        
+                        kwargs = (; schedule, split, nchunks)
+                        if (split == :scatter || schedule == :greedy) || op ∉ (vcat, *)
+                            # scatter and greedy only works for commutative operators!
+                        else
+                            mapreduce_f_op_itr = mapreduce(f, op, itrs...)
+                            @test tmapreduce(f, op, itrs...; init, kwargs...) ~ mapreduce_f_op_itr
+                            @test treducemap(op, f, itrs...; init, kwargs...) ~ mapreduce_f_op_itr
+                            @test treduce(op, f.(itrs...); init, kwargs...) ~ mapreduce_f_op_itr
+                        end
+                        
+                        map_f_itr = map(f, itrs...)
+                        @test all(tmap(f, Any, itrs...; kwargs...) .~ map_f_itr)
+                        @test all(tcollect(Any, (f(x...) for x in collect(zip(itrs...))); kwargs...) .~ map_f_itr)
+                        @test all(tcollect(Any, f.(itrs...); kwargs...) .~ map_f_itr)
+                        
+                        RT = Core.Compiler.return_type(f, Tuple{eltype.(itrs)...})
+                            
+                        @test tmap(f, RT, itrs...; kwargs...) ~ map_f_itr
+                        @test tcollect(RT, (f(x...) for x in collect(zip(itrs...))); kwargs...) ~ map_f_itr
+                        @test tcollect(RT, f.(itrs...); kwargs...) ~ map_f_itr
+                        
+                        if schedule !== :greedy
+                            @test tmap(f, itrs...; kwargs...) ~ map_f_itr
+                            @test tcollect((f(x...) for x in collect(zip(itrs...))); kwargs...) ~ map_f_itr
+                            @test tcollect(f.(itrs...); kwargs...) ~ map_f_itr
+                        end
+                    end
                 end
             end
         end