diff --git a/src/TensorNetwork.jl b/src/TensorNetwork.jl
index 729dade90..8e04b58cf 100644
--- a/src/TensorNetwork.jl
+++ b/src/TensorNetwork.jl
@@ -91,6 +91,7 @@ Return the names of the indices in the [`TensorNetwork`](@ref).
       + `:open` Indices only mentioned in one tensor.
       + `:inner` Indices mentioned at least twice.
       + `:hyper` Indices mentioned at least in three tensors.
+      + `:parallel` Indices parallel to `i` in the graph (`i` included).
 """
 Tenet.inds(tn::TensorNetwork; set::Symbol=:all, kwargs...) = inds(tn, set; kwargs...)
 @valsplit 2 Tenet.inds(tn::TensorNetwork, set::Symbol, args...) = throw(MethodError(inds, "unknown set=$set"))
@@ -111,6 +112,10 @@ function Tenet.inds(tn::TensorNetwork, ::Val{:hyper})
     return map(first, Iterators.filter(((_, v),) -> length(v) >= 3, tn.indexmap))
 end
 
+function Tenet.inds(tn::TensorNetwork, ::Val{:parallel}, i::Symbol)
+    return mapreduce(inds, ∩, select(tn, :containing, i))
+end
+
 """
     size(tn::TensorNetwork)
     size(tn::TensorNetwork, index)
diff --git a/src/Transformations.jl b/src/Transformations.jl
index 03413de13..ef956bb21 100644
--- a/src/Transformations.jl
+++ b/src/Transformations.jl
@@ -103,6 +103,49 @@ function transform!(tn::TensorNetwork, ::HyperGroup)
     end
 end
 
+"""
+    RankSimplification <: Transformation
+
+Preemptively contract tensors whose result doesn't increase in size.
+"""
+@kwdef struct RankSimplification <: Transformation
+    minimize::Symbol = :length
+
+    function RankSimplification(minimize::Symbol)
+        @assert minimize in (:length, :rank)
+        return new(minimize)
+    end
+end
+
+function transform!(tn::TensorNetwork, config::RankSimplification)
+    # select indices that benefit from contraction
+    targets = filter(inds(tn; set=:inner)) do index
+        candidate_tensors = select(tn, :containing, index)
+
+        # check that the contraction minimizes the size/rank
+        result = sum([
+            EinExpr(inds(tensor), Dict(index => size(tensor, index) for index in inds(tensor))) for
+            tensor in candidate_tensors
+        ])
+
+        if config.minimize == :rank
+            return ndims(result) <= minimum(ndims, candidate_tensors)
+        end
+
+        return length(result) <= minimum(length, candidate_tensors)
+    end
+
+    # group parallel indices
+    targets = unique(Iterators.map(x -> inds(tn, :parallel, x), targets))
+
+    # contract target indices
+    for target in targets
+        contract!(tn, target)
+    end
+
+    return tn
+end
+
 """
     DiagonalReduction <: Transformation
 
@@ -152,45 +195,6 @@ function transform!(tn::TensorNetwork, config::DiagonalReduction)
     return tn
 end
 
-"""
-    RankSimplification <: Transformation
-
-Preemptively contract tensors whose result doesn't increase in size.
-"""
-struct RankSimplification <: Transformation end
-
-function transform!(tn::TensorNetwork, ::RankSimplification)
-    @label rank_transformation_start
-    for tensor in tensors(tn)
-        # TODO replace this code for `neighbours` method
-        connected_tensors = mapreduce(label -> select(tn, :any, label), ∪, inds(tensor))
-        filter!(!=(tensor), connected_tensors)
-
-        for c_tensor in connected_tensors
-            # TODO keep output inds?
-            path = sum([
-                EinExpr(inds(tensor), Dict(index => size(tensor, index) for index in inds(tensor))) for
-                tensor in [tensor, c_tensor]
-            ])
-
-            # Check if contraction does not increase the rank
-            EinExprs.removedsize(path) < 0 && continue
-
-            new_tensor = contract(tensor, c_tensor)
-
-            # Update tensor network
-            push!(tn, new_tensor)
-            delete!(tn, tensor)
-            delete!(tn, c_tensor)
-
-            # Break the loop since we modified the network and need to recheck connections
-            @goto rank_transformation_start
-        end
-    end
-
-    return tn
-end
-
 """
     AntiDiagonalGauging <: Transformation