diff --git a/README.md b/README.md
index 234f26fa..24b38d84 100644
--- a/README.md
+++ b/README.md
@@ -109,6 +109,7 @@ unimplemented for the last 15 years of publications including:
 | Surrogate Outcomes              | [Tikka and Karvanen, 2018](https://arxiv.org/abs/1806.07172)                        |
 | Counterfactual Transportability | [Correia, Lee, Bareinboim, 2022](https://proceedings.mlr.press/v162/correa22a.html) |
 | Cyclic ID                       | [Forré and Mooij, 2019](https://arxiv.org/abs/1901.00433v2)                         |
+| Cyclic IDC                      | _ours_                                                                              |
 
 Apply an algorithm to an Acyclic Directed Mixed Graph (ADMG) and a causal query
 to generate an estimand represented in the DSL like:
diff --git a/src/y0/algorithm/do_calculus.py b/src/y0/algorithm/do_calculus.py
index f7d5a89e..0fdd507a 100644
--- a/src/y0/algorithm/do_calculus.py
+++ b/src/y0/algorithm/do_calculus.py
@@ -1,8 +1,9 @@
 """Do Calculus."""
 
-from typing import Annotated
+from typing import Annotated, Literal
 
 from .conditional_independencies import are_d_separated
+from .separation import are_sigma_separated
 from ..dsl import Variable
 from ..graph import NxMixedGraph
 from ..util import InPaperAs
@@ -23,6 +24,7 @@ def rule_2_of_do_calculus_applies(
     outcomes: Annotated[set[Variable], InPaperAs(r"\mathbf{Y}")],
     conditions: Annotated[set[Variable], InPaperAs(r"\mathbf{Z}")],
     condition: Variable,
+    separation_implementation: Literal["d", "sigma"] | None = None,
 ) -> bool:
     r"""Check if Rule 2 of the Do-Calculus applies to the conditioned variable.
 
@@ -31,6 +33,8 @@ def rule_2_of_do_calculus_applies(
     :param conditions:
     :param outcomes:
     :param condition: The condition to check
+    :param separation_implementation: The separation implementation. Defaults to d
+        separation, but can be generalized to sigma separation
 
     :returns: If rule 2 applies, see below.
 
@@ -50,7 +54,15 @@ def rule_2_of_do_calculus_applies(
     reduced_graph: Annotated[NxMixedGraph, InPaperAs(r"G_{\bar{x}, \underbar{z}}")] = (
         graph.remove_in_edges(treatments).remove_out_edges(condition)
     )
-    return all(
-        are_d_separated(reduced_graph, outcome, condition, conditions=reduced_conditions)
-        for outcome in outcomes
-    )
+    if separation_implementation == "d" or separation_implementation is None:
+        return all(
+            are_d_separated(reduced_graph, outcome, condition, conditions=reduced_conditions)
+            for outcome in outcomes
+        )
+    elif separation_implementation == "sigma":
+        return all(
+            are_sigma_separated(reduced_graph, outcome, condition, conditions=reduced_conditions)
+            for outcome in outcomes
+        )
+    else:
+        raise ValueError(f"Unknown separation implementation: {separation_implementation}")
diff --git a/src/y0/algorithm/identify/__init__.py b/src/y0/algorithm/identify/__init__.py
index 26ca579b..723c8c99 100644
--- a/src/y0/algorithm/identify/__init__.py
+++ b/src/y0/algorithm/identify/__init__.py
@@ -13,6 +13,7 @@
 ID* [shpitser2012]_    :mod:`y0.algorithm.identify.id_star`
 IDC* [shpitser2012]_   :mod:`y0.algorithm.identify.idc_star`
 Cyclic ID [forre2019]_ :mod:`y0.algorithm.identify.cyclic_id`
+Cyclic IDC             :mod:`y0.algorithm.identify.cyclic_idc`
 gID [correa2019]_      `Issue #72
                        <https://github.com/y0-causal-inference/y0/issues/72>`_
 gID* [correa2021]_     `Issue #121
@@ -71,6 +72,7 @@
 
 from .api import identify_outcomes
 from .cyclic_id import cyclic_id
+from .cyclic_idc import cyclic_idc
 from .id_c import idc
 from .id_star import id_star
 from .id_std import identify
@@ -82,6 +84,7 @@
     "Query",
     "Unidentifiable",
     "cyclic_id",
+    "cyclic_idc",
     "id_star",
     "idc",
     "idc_star",
diff --git a/src/y0/algorithm/identify/cyclic_idc.py b/src/y0/algorithm/identify/cyclic_idc.py
new file mode 100644
index 00000000..620d9689
--- /dev/null
+++ b/src/y0/algorithm/identify/cyclic_idc.py
@@ -0,0 +1,54 @@
+"""An implementation of Cyclic IDC, based off of the extension from ID to IDC."""
+
+from collections.abc import Iterable, Sequence
+
+from .cyclic_id import cyclic_id
+from .utils import Identification
+from ..do_calculus import rule_2_of_do_calculus_applies
+from ...dsl import Expression, Variable
+from ...graph import NxMixedGraph
+
+__all__ = ["cyclic_idc"]
+
+
+def cyclic_idc(
+    graph: NxMixedGraph,
+    outcomes: Variable | Iterable[Variable],
+    interventions: Variable | Iterable[Variable],
+    conditions: Variable | Iterable[Variable],
+    *,
+    ordering: Sequence[Variable] | None = None,
+) -> Expression:
+    """Run cyclic ID with support for conditions."""
+    identification = Identification.from_parts(
+        graph=graph,
+        outcomes=outcomes,
+        treatments=interventions,
+        conditions=conditions,
+    )
+    for condition in identification.conditions:
+        if rule_2_of_do_calculus_applies(
+            graph=identification.graph,
+            treatments=identification.treatments,
+            outcomes=identification.outcomes,
+            conditions=identification.conditions,
+            condition=condition,
+            separation_implementation="sigma",
+        ):
+            modified = identification.exchange_observation_with_action(condition)
+            return cyclic_idc(
+                graph=modified.graph,
+                outcomes=modified.outcomes,
+                interventions=modified.treatments,
+                conditions=modified.conditions,
+                ordering=ordering,
+            )
+
+    modified = identification.uncondition()
+    id_estimand = cyclic_id(
+        graph=modified.graph,
+        outcomes=modified.outcomes,
+        interventions=modified.treatments,
+        ordering=ordering,
+    )
+    return id_estimand.normalize_marginalize(identification.outcomes)