diff --git a/cpmpy/tools/explain/mus.py b/cpmpy/tools/explain/mus.py
index 6fa385dba..4899e277e 100644
--- a/cpmpy/tools/explain/mus.py
+++ b/cpmpy/tools/explain/mus.py
@@ -1,9 +1,10 @@
 """
-    Re-impementation of MUS-computation techniques in CPMPy
+    Re-implementation of MUS-computation techniques in CPMPy
 
     - Deletion-based MUS
     - QuickXplain
     - Optimal MUS
+    - IIS-based MUS extraction
 """
 import warnings
 import numpy as np
@@ -330,6 +331,47 @@ def optimal_mus_naive(soft, hard=[], weights=None, solver="ortools", hs_solver="
     """
     return ocus_naive(soft, hard, weights, meta_constraint=True, solver=solver, hs_solver=hs_solver)
 
-   
 
+def mus_iis(soft, hard=[], solver="gurobi"):
+    """
+        Compute a MUS using a ILP solver's native Irreducible Inconsistent Subsystem (IIS) algorithm (ILP term equivalent to MUS)
+
+        :param soft: soft constraints, list of expressions
+        :param hard: hard constraints, optional, list of expressions
+        :param solver: which ILP solver to use (only `gurobi` supported)
+    """
+    assert solver == "gurobi", f"Only Gurobi supported as IIS solver, but was given {solver}"
+
+    # Create assumption variables and model with hard + (assumption -> soft)
+    m, soft, assumptions = make_assump_model(soft, hard)
+
+    # Instantiate solver (will check if solver is installed and licensed)
+    s = cp.SolverLookup.get(solver, m)
+    grb_model = s.grb_model
+
+    # Force all hard constraints into the IIS (1 = force in, 0 = force out, -1 (default) = soft), as well as all `a -> c` for each assumption `a` and constraint `c` of each group/soft constraint in `soft`
+    grb_model.update()  # update required ; otherwise `getConstrs` can return empty
+    for hard_constraint in grb_model.getConstrs():
+        hard_constraint.IISConstrForce = 1
+    for hard_constraint in grb_model.getGenConstrs():  # CPMpy also posts general constraints
+        hard_constraint.IISGenConstrForce = 1
+
+    # Add each assumption as a soft constraint `a>=1` using Gurobi directly (as opposed to e.g. `s+=assumptions`), in order to gain access to the returned Gurobi constraints so we can access their `IISConstr` later
+    # Gurobi returns its own `tupledict`, we just need the constraints (i.e. values)
+
+    # Get solver variables first and update model to register any newly created variables
+    solver_assumptions = s.solver_vars(assumptions)
+    grb_model.update()
+    grb_assumptions = grb_model.addConstrs(a >= 1 for a in solver_assumptions).values()
+
+    import gurobipy  # Safe to import gurobipy since instantiating the Gurobi solver succeeded
+    try:
+        grb_model.computeIIS()
+    except gurobipy.GurobiError as e:
+        if e.errno == gurobipy.GRB.Error.IIS_NOT_INFEASIBLE:
+            raise AssertionError("MUS: model must be UNSAT")
+        raise
+
+    # Find which assumption is in the IIS/MUS
+    return [soft for soft, grb_assumption in zip(soft, grb_assumptions) if grb_assumption.IISConstr]
 
diff --git a/tests/test_tools_mus.py b/tests/test_tools_mus.py
index 0c5215754..0d7c02be3 100644
--- a/tests/test_tools_mus.py
+++ b/tests/test_tools_mus.py
@@ -2,7 +2,7 @@
 
 import cpmpy as cp
 from cpmpy.tools import mss_opt, marco, OCUSException
-from cpmpy.tools.explain import mus, mus_naive, quickxplain, quickxplain_naive, optimal_mus, optimal_mus_naive, mss, mcs, ocus, ocus_naive
+from cpmpy.tools.explain import mus, mus_naive, quickxplain, quickxplain_naive, optimal_mus, optimal_mus_naive, mss, mcs, ocus, ocus_naive, mus_iis
 
 
 class TestMus:
@@ -84,6 +84,22 @@ def test_wglobal(self):
         assert not cp.Model(ms).solve()
         # self.assertEqual(set(self.naive_func(cons)), set(cons[:2]))
 
+    def test_decomposed_global(self):
+        x = cp.intvar(1, 5, shape=3, name="x")
+        soft = [x[0] == x[1], x[1] == x[2]]
+        hard = [cp.AllDifferent(x)]
+
+        mus_cons = self.mus_func(soft=soft, hard=hard)
+        assert len(set(mus_cons)) == 1
+        mus_naive_cons = self.naive_func(soft=soft, hard=hard)
+        assert len(set(mus_naive_cons)) == 1
+
+
+@pytest.mark.requires_solver("gurobi")
+class TestIIS(TestMus):
+    def setup_method(self):
+        self.mus_func = lambda soft, hard=[], solver="gurobi": mus_iis(soft, hard=hard, solver="gurobi")
+        self.naive_func = mus_naive
 
 class TestQuickXplain(TestMus):
 
@@ -219,4 +235,4 @@ def test_circular(self):
             x[3] > x[0],
             (x[3] > x[1]).implies((x[3] > x[2]) & ((x[3] == 3) | (x[1] == x[2])))
         ]
-        assert len(mcs(cons)) == 1
\ No newline at end of file
+        assert len(mcs(cons)) == 1