diff --git a/debug/debug_compress_approximations.py b/debug/debug_compress_approximations.py
new file mode 100644
index 00000000..4c0fb8c1
--- /dev/null
+++ b/debug/debug_compress_approximations.py
@@ -0,0 +1,33 @@
+from cProfile import label
+from lsqecc.gates.compress_rotation_approximations import partition_gate_sequence
+from lsqecc.pauli_rotations.rotation import CachedRotationApproximations
+from lsqecc.gates.pi_over_2_to_the_n_rz_gate_approximations import get_pi_over_2_to_the_n_rz_gate
+import numpy as np
+import matplotlib.pyplot as plt
+
+# test_sequence_1 = "SSSXHSTHTHSTHTH"
+# test_sequence_2 = "SHSSXH"
+# test_sequence_3 = "HSSTTSHSH"
+test_sequence = CachedRotationApproximations.get_pi_over_2_to_the_n_rz_gate(3)
+sequences_Z = partition_gate_sequence(test_sequence)
+sequences_X = partition_gate_sequence("H" + test_sequence + "H")
+
+print("The gate for a Z rotation are:\n")
+print(f"The number of gates without compression in Gate Frame of is {len(test_sequence)} ")
+print(
+    f"Number of gates without compressiopn in Pauli Frame is {len(test_sequence) + 2*test_sequence.count('H')}"
+)
+print(f"The number of partitions (Compressed list of gates) is {len(sequences_Z)}")
+
+print("The gate for a X rotation are:\n")
+print(f"The number of gates without compression in Gate Frame of is {len(test_sequence)+2} ")
+print(
+    f"Number of gates without compressiopn in Pauli Frame is {len(test_sequence) + 2*test_sequence.count('H') + 6}"
+)
+print(f"The number of partitions (Compressed list of gates) is {len(sequences_X)}")
+
+
+# for seq in sequences:
+#     print(f"{seq}")
+
+# Most common ones are HTH and HSTH
diff --git a/debug/debug_to_basic_form_compress.py b/debug/debug_to_basic_form_compress.py
new file mode 100644
index 00000000..3bc85d9c
--- /dev/null
+++ b/debug/debug_to_basic_form_compress.py
@@ -0,0 +1,12 @@
+from lsqecc.pauli_rotations.rotation import PauliRotation, PauliOperator
+from fractions import Fraction
+
+Z = PauliOperator.Z
+uncompressed_list = PauliRotation.from_list([Z], Fraction(1, 16)).to_basic_form_decomposition(
+    compress_rotations=False
+)
+print(len(uncompressed_list))
+compressed_list = PauliRotation.from_list([Z], Fraction(1, 16)).to_basic_form_decomposition(
+    compress_rotations=True
+)
+print(len(compressed_list))
diff --git a/src/lsqecc/gates/compress_rotation_approximations.py b/src/lsqecc/gates/compress_rotation_approximations.py
new file mode 100644
index 00000000..ffa6f66f
--- /dev/null
+++ b/src/lsqecc/gates/compress_rotation_approximations.py
@@ -0,0 +1,36 @@
+def partition_gate_sequence(gate_approximation: str):
+    partitioned_sequence = list()
+    partition = ""
+    in_x_basis = False
+
+    # note: The sequence 'HXH' is not covered by this function.
+    # But this also not encountered in the cached rotations
+    for index, gate in enumerate(gate_approximation):
+        if gate in {"S", "T"}:
+            partition += gate
+        elif gate == "X":
+            if not len(partition):  # empty partition
+                pass
+            elif partition[0] == "H":
+                partitioned_sequence.append(partition[0])
+                partitioned_sequence.append(partition[1:])
+            else:
+                partitioned_sequence.append(partition)
+            partitioned_sequence.append(gate)
+            partition = ""
+
+        elif gate == "H":
+            if not in_x_basis:
+                if not len(partition) == 0:
+                    partitioned_sequence.append(partition)
+                partition = gate
+                if index == len(gate_approximation) - 1:
+                    partitioned_sequence.append(partition)
+                in_x_basis = True
+            else:
+                partition += gate
+                in_x_basis = False
+                partitioned_sequence.append(partition)
+                partition = ""
+
+    return partitioned_sequence
diff --git a/src/lsqecc/pauli_rotations/rotation.py b/src/lsqecc/pauli_rotations/rotation.py
index 38e89c48..0b3b2bac 100644
--- a/src/lsqecc/pauli_rotations/rotation.py
+++ b/src/lsqecc/pauli_rotations/rotation.py
@@ -23,6 +23,7 @@
 from typing import Dict, List, Tuple
 
 import lsqecc.simulation.conditional_operation_control as coc
+from lsqecc.gates.compress_rotation_approximations import partition_gate_sequence
 from lsqecc.gates.pi_over_2_to_the_n_rz_gate_approximations import (
     get_pi_over_2_to_the_n_rz_gate,
 )
@@ -234,7 +235,9 @@ def __eq__(self, other) -> bool:
     def __hash__(self) -> int:
         return hash(hash(self.rotation_amount) + hash(tuple(self.ops_list)))
 
-    def to_basic_form_approximation(self) -> List["PauliRotation"]:
+    def to_basic_form_approximation(
+        self, compress_rotations: bool = False
+    ) -> List["PauliRotation"]:
         """Get an approximation in terms of pi/2, pi/4 and pi/8"""
 
         if not is_power_of_two(self.rotation_amount.denominator):
@@ -247,7 +250,6 @@ def to_basic_form_approximation(self) -> List["PauliRotation"]:
             int(math.log2(self.rotation_amount.denominator))
             - 1
         )
-
         axis_list = list(filter(lambda op: op != PauliOperator.I, self.ops_list))
         if len(axis_list) != 1:
             raise Exception("Can only approximate single qubit rotations")
@@ -260,6 +262,8 @@ def to_basic_form_approximation(self) -> List["PauliRotation"]:
         else:
             raise Exception(f"Unsupported axis of rotation {axis}")
 
+        if compress_rotations:
+            approximation_gates = partition_gate_sequence(approximation_gates)
         rotations = []
         qubit_idx = self.ops_list.index(axis)
         for gate in approximation_gates:
@@ -271,13 +275,24 @@ def to_basic_form_approximation(self) -> List["PauliRotation"]:
                 rotations.append(PauliRotation.from_x_gate(self.qubit_num, qubit_idx))
             elif gate == "H":
                 rotations.extend(PauliRotation.from_hadamard_gate(self.qubit_num, qubit_idx))
+            elif len(gate) > 1:
+                rotations.append(PauliRotation.from_gate_string(self.qubit_num, qubit_idx, gate))
             else:
                 raise Exception(f"Cannot decompose gate: {gate}")
 
         # Note that it might be possible to simplify these a little further
         return rotations
 
-    def to_basic_form_decomposition(self) -> List["PauliRotation"]:
+    @staticmethod
+    def count_s_and_t_to_phase(gate_string: str) -> Fraction:
+        s_count = gate_string.count("S")
+        t_count = gate_string.count("T")
+        phase = s_count * Fraction(1, 2) + t_count * Fraction(1, 4)
+        return phase
+
+    def to_basic_form_decomposition(
+        self, compress_rotations: bool = False
+    ) -> List["PauliRotation"]:
         """Express in terms of pi/2, pi/4 and pi/8"""
         if self.rotation_amount.denominator == 1:
             return []  # don't need to do anything because exp(-i*pi*P) = I
@@ -292,7 +307,7 @@ def to_basic_form_decomposition(self) -> List["PauliRotation"]:
                     output_rotations.append(new_rotation)
             return output_rotations
         else:
-            return self.to_basic_form_approximation()
+            return self.to_basic_form_approximation(compress_rotations)
 
     def to_latex(self) -> str:
         return f"{super().to_latex()}_{{{phase_frac_to_latex(self.rotation_amount)}}}"
@@ -307,6 +322,23 @@ def from_list(pauli_ops: List[PauliOperator], rotation: Fraction) -> "PauliRotat
             r.change_single_op(i, op)
         return r
 
+    @staticmethod
+    def from_gate_string(num_qubits: int, target_qubit: int, gate_string: str):
+        if gate_string.startswith("H") and gate_string.endswith("H"):
+            return PauliRotation.from_r_gate(
+                num_qubits,
+                target_qubit,
+                PauliOperator.X,
+                phase=PauliRotation.count_s_and_t_to_phase(gate_string),
+            )
+        else:
+            return PauliRotation.from_r_gate(
+                num_qubits,
+                target_qubit,
+                PauliOperator.Z,
+                phase=PauliRotation.count_s_and_t_to_phase(gate_string),
+            )
+
     @staticmethod
     def from_r_gate(num_qubits: int, target_qubit: int, phase_type: PauliOperator, phase: Fraction):
         """Note that the convention for rz and rx is different from our pauli rotation convention.
diff --git a/src/lsqecc/resource_estimation/gate_count_compression_analysis.py b/src/lsqecc/resource_estimation/gate_count_compression_analysis.py
new file mode 100644
index 00000000..c67c65e4
--- /dev/null
+++ b/src/lsqecc/resource_estimation/gate_count_compression_analysis.py
@@ -0,0 +1,76 @@
+import matplotlib.pyplot as plt
+import numpy as np
+
+from lsqecc.gates.compress_rotation_approximations import partition_gate_sequence
+from lsqecc.gates.pi_over_2_to_the_n_rz_gate_approximations import (
+    get_pi_over_2_to_the_n_rz_gate,
+)
+
+gate_counts_Z = np.zeros((len(get_pi_over_2_to_the_n_rz_gate[3:]), 3))
+for index, gate_sequence in enumerate(get_pi_over_2_to_the_n_rz_gate[3:]):
+    compressed_sequence = partition_gate_sequence(gate_sequence)
+    gate_counts_Z[index, 0] = len(gate_sequence)
+    gate_counts_Z[index, 1] = len(gate_sequence) + 2 * gate_sequence.count("H")
+    gate_counts_Z[index, 2] = len(compressed_sequence)
+
+gate_counts_X = np.zeros((len(get_pi_over_2_to_the_n_rz_gate[3:]), 3))
+for index, gate_sequence in enumerate(get_pi_over_2_to_the_n_rz_gate[3:]):
+    compressed_sequence = partition_gate_sequence("H" + gate_sequence + "H")
+    gate_counts_X[index, 0] = len(gate_sequence)
+    gate_counts_X[index, 1] = len(gate_sequence) + 2 * gate_sequence.count("H") + 6
+    gate_counts_X[index, 2] = len(compressed_sequence)
+
+
+compression_ratio_mean_Z = np.mean(np.divide(gate_counts_Z[:, 1], gate_counts_Z[:, 2]))
+compression_ratio_mean_X = np.mean(np.divide(gate_counts_X[:, 1], gate_counts_X[:, 2]))
+
+
+plt.figure(figsize=(16, 9))
+plt.plot(
+    np.arange(0, len(get_pi_over_2_to_the_n_rz_gate[3:])),
+    gate_counts_Z[:, 0],
+    label="Uncompressed Gate Count: Gate Frame",
+)
+plt.plot(
+    np.arange(0, len(get_pi_over_2_to_the_n_rz_gate[3:])),
+    gate_counts_Z[:, 1],
+    label="Uncompressed Gate Count: Pauli Frame",
+)
+plt.plot(
+    np.arange(0, len(get_pi_over_2_to_the_n_rz_gate[3:])),
+    gate_counts_Z[:, 2],
+    label="Compressed Gate Count: Pauli Frame",
+)
+plt.xlabel("Rotation amount (in powers of 2)")
+plt.ylabel("Gate Count")
+plt.title(
+    "Compression of Z Rotation gates in Pauli Frame \n"
+    + f" Mean Compression Ratio = ={compression_ratio_mean_Z}"
+)
+plt.legend()
+# plt.savefig("assets/compression_Z_rotations.png")
+
+plt.figure(figsize=(16, 9))
+plt.plot(
+    np.arange(0, len(get_pi_over_2_to_the_n_rz_gate[3:])),
+    gate_counts_X[:, 0],
+    label="Uncompressed Gate Count: Gate Frame",
+)
+plt.plot(
+    np.arange(0, len(get_pi_over_2_to_the_n_rz_gate[3:])),
+    gate_counts_X[:, 1],
+    label="Uncompressed Gate Count: Pauli Frame",
+)
+plt.plot(
+    np.arange(0, len(get_pi_over_2_to_the_n_rz_gate[3:])),
+    gate_counts_X[:, 2],
+    label="Compressed Gate Count: Pauli Frame",
+)
+plt.xlabel("Rotation amount (in powers of 2)")
+plt.ylabel("Gate Count")
+plt.title(
+    "Compression of X Rotation gates in Pauli Frame \n"
+    + f"Mean Compression Ratio = ={compression_ratio_mean_X}"
+)
+plt.legend()
+# plt.savefig("assets/compression_X_rotations.png")
diff --git a/tests/gates/compress_rotation_approximations_test.py b/tests/gates/compress_rotation_approximations_test.py
new file mode 100644
index 00000000..12ba9a8c
--- /dev/null
+++ b/tests/gates/compress_rotation_approximations_test.py
@@ -0,0 +1,21 @@
+from typing import List
+
+import pytest
+
+from lsqecc.gates.compress_rotation_approximations import partition_gate_sequence
+
+
+class TestGateCompression:
+    @pytest.mark.parametrize(
+        "gate_string, partitioned_gates",
+        [
+            ("SSSXHSTHTHSTHTH", ["SSS", "X", "HSTH", "T", "HSTH", "T", "H"]),
+            ("SHSSXH", ["S", "H", "SS", "X", "H"]),
+            ("HSSTTSHSX", ["HSSTTSH", "S", "X"]),
+            ("STXH", ["ST", "X", "H"]),
+        ],
+    )
+    def test_partition_gate_sequence(self, gate_string: str, partitioned_gates: List[str]):
+        func_output = partition_gate_sequence(gate_string)
+        assert len(partitioned_gates) == len(func_output)
+        assert func_output == partitioned_gates
diff --git a/tests/pauli_rotations/rotation_test.py b/tests/pauli_rotations/rotation_test.py
index b59f5199..c682d6a2 100644
--- a/tests/pauli_rotations/rotation_test.py
+++ b/tests/pauli_rotations/rotation_test.py
@@ -215,6 +215,24 @@ def test_to_basic_form_decomposition_with_approximation(self, snapshot):
             "list_repr.txt",
         )
 
+    def test_to_basic_form_decomposition_with_approximation_and_compression(self, snapshot):
+        snapshot.assert_match(
+            repr(
+                PauliRotation.from_list([Z], Fraction(1, 16)).to_basic_form_decomposition(
+                    compress_rotations=True
+                )
+            ),
+            "list_repr_Z.txt",
+        )
+        snapshot.assert_match(
+            repr(
+                PauliRotation.from_list([X], Fraction(1, 16)).to_basic_form_decomposition(
+                    compress_rotations=True
+                )
+            ),
+            "list_repr_X.txt",
+        )
+
     @pytest.mark.parametrize(
         "rotation",
         [
diff --git a/tests/pauli_rotations/snapshots/rotation_test/test_to_basic_form_decomposition_with_approximation_and_compression/list_repr_X.txt b/tests/pauli_rotations/snapshots/rotation_test/test_to_basic_form_decomposition_with_approximation_and_compression/list_repr_X.txt
new file mode 100644
index 00000000..5291896a
--- /dev/null
+++ b/tests/pauli_rotations/snapshots/rotation_test/test_to_basic_form_decomposition_with_approximation_and_compression/list_repr_X.txt
@@ -0,0 +1 @@
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diff --git a/tests/pauli_rotations/snapshots/rotation_test/test_to_basic_form_decomposition_with_approximation_and_compression/list_repr_Z.txt b/tests/pauli_rotations/snapshots/rotation_test/test_to_basic_form_decomposition_with_approximation_and_compression/list_repr_Z.txt
new file mode 100644
index 00000000..cad9dda5
--- /dev/null
+++ b/tests/pauli_rotations/snapshots/rotation_test/test_to_basic_form_decomposition_with_approximation_and_compression/list_repr_Z.txt
@@ -0,0 +1 @@
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