diff --git a/src/y0/dsl.py b/src/y0/dsl.py
index 148e047..6247e6a 100644
--- a/src/y0/dsl.py
+++ b/src/y0/dsl.py
@@ -15,8 +15,7 @@ __all__ = [
     'Variable',
     'Intervention',
     'CounterfactualVariable',
-    'ConditionalProbability',
-    'JointProbability',
+    'Distribution',
     'P',
     'Probability',
     'Sum',
@@ -44,6 +43,9 @@ class _Mathable(ABC):
     def to_latex(self) -> str:
         """Output this DSL object in the LaTeX string format."""
 
+    def _repr_latex_(self) -> str:  # hack for auto-display of latex in jupyter notebook
+        return f'${self.to_latex()}$'
+
     def __str__(self) -> str:
         return self.to_text()
 
@@ -84,23 +86,36 @@ class Variable(_Mathable):
     def __matmul__(self, variables: XList[Variable]) -> CounterfactualVariable:
         return self.intervene(variables)
 
-    def given(self, parents: XList[Variable]) -> ConditionalProbability:
+    def given(self, parents: Union[XList[Variable], Distribution]) -> Distribution:
         """Create a distribution in which this variable is conditioned on the given variable(s).
 
+        The new distribution is a Markov Kernel.
+
         :param parents: A variable or list of variables to include as conditions in the new conditional distribution
         :returns: A new conditional probability distribution
+        :raises TypeError: If a distribution is given as the parents that contains conditionals
 
         .. note:: This function can be accessed with the or | operator.
         """
-        return ConditionalProbability(
-            child=self,
-            parents=_upgrade_variables(parents),
-        )
-
-    def __or__(self, parents: XList[Variable]) -> ConditionalProbability:
+        if not isinstance(parents, Distribution):
+            return Distribution(
+                children=[self],
+                parents=_upgrade_variables(parents),
+            )
+        elif parents.is_conditioned():
+            raise TypeError('can not be given a distribution that has conditionals')
+        else:
+            # The parents variable is actually a Distribution instance with no parents,
+            #  so its children become the parents for the new Markov Kernel distribution
+            return Distribution(
+                children=[self],
+                parents=parents.children,  # don't think about this too hard
+            )
+
+    def __or__(self, parents: XList[Variable]) -> Distribution:
         return self.given(parents)
 
-    def joint(self, children: XList[Variable]) -> JointProbability:
+    def joint(self, children: XList[Variable]) -> Distribution:
         """Create a joint distribution between this variable and the given variable(s).
 
         :param children: The variable(s) for use with this variable in a joint distribution
@@ -108,9 +123,11 @@ class Variable(_Mathable):
 
         .. note:: This function can be accessed with the and & operator.
         """
-        return JointProbability([self, *_upgrade_variables(children)])
+        return Distribution(
+            children=[self, *_upgrade_variables(children)],
+        )
 
-    def __and__(self, children: XList[Variable]) -> JointProbability:
+    def __and__(self, children: XList[Variable]) -> Distribution:
         return self.joint(children)
 
     def invert(self) -> Intervention:
@@ -211,82 +228,97 @@ class CounterfactualVariable(Variable):
 
 
 @dataclass
-class JointProbability(_Mathable):
-    """A joint probability distribution over several variables."""
+class Distribution(_Mathable):
+    """A general distribution over several child variables, conditioned by several parents."""
 
     children: List[Variable]
+    parents: List[Variable] = field(default_factory=list)
+
+    def __post_init__(self):
+        if isinstance(self.children, Variable):
+            self.children = [self.children]
+        if not self.children:
+            raise ValueError('distribution must have at least one child')
+        if isinstance(self.parents, Variable):
+            self.parents = [self.parents]
 
     def to_text(self) -> str:
-        """Output this joint probability distribution in the internal string format."""
-        return ','.join(child.to_text() for child in self.children)
+        """Output this distribution in the internal string format."""
+        children = ','.join(child.to_text() for child in self.children)
+        if self.parents:
+            parents = ','.join(parent.to_text() for parent in self.parents)
+            return f'{children}|{parents}'
+        else:
+            return children
 
     def to_latex(self) -> str:
-        """Output this joint probability distribution in the LaTeX string format."""
-        return ','.join(child.to_latex() for child in self.children)
+        """Output this distribution in the LaTeX string format."""
+        children = ','.join(child.to_latex() for child in self.children)
+        parents = ','.join(parent.to_latex() for parent in self.parents)
+        return f'{children}|{parents}'
+
+    def is_conditioned(self) -> bool:
+        """Return if this distribution is conditioned."""
+        return 0 < len(self.parents)
 
-    def joint(self, children: XList[Variable]) -> JointProbability:
-        """Create a joint distribution between the variables in this distribution the given variable(s).
+    def is_markov_kernel(self) -> bool:
+        """Return if this distribution a markov kernel -> one child variable and one or more conditionals."""
+        return len(self.children) == 1
 
-        :param children: The variable(s) with which this joint distribution is extended
-        :returns: A new joint distribution over all previous and given variables.
+    def joint(self, children: XList[Variable]) -> Distribution:
+        """Create a new distribution including the given child variables.
+
+        :param children: The variable(s) with which this distribution's children are extended
+        :returns: A new distribution.
 
         .. note:: This function can be accessed with the and & operator.
         """
-        return JointProbability([
-            *self.children,
-            *_upgrade_variables(children),
-        ])
+        return Distribution(
+            children=[*self.children, *_upgrade_variables(children)],
+            parents=self.parents,
+        )
 
-    def __and__(self, children: XList[Variable]) -> JointProbability:
+    def __and__(self, children: XList[Variable]) -> Distribution:
         return self.joint(children)
 
+    def given(self, parents: Union[XList[Variable], Distribution]) -> Distribution:
+        """Create a new mixed distribution additionally conditioned on the given parent variables.
 
-@dataclass
-class ConditionalProbability(_Mathable):
-    """A conditional distribution over a single child variable and one or more parent conditional variables."""
-
-    child: Variable
-    parents: List[Variable]
-
-    def to_text(self) -> str:
-        """Output this conditional probability distribution in the internal string format."""
-        parents = ','.join(parent.to_text() for parent in self.parents)
-        return f'{self.child.to_text()}|{parents}'
-
-    def to_latex(self) -> str:
-        """Output this conditional probability distribution in the LaTeX string format."""
-        parents = ','.join(parent.to_latex() for parent in self.parents)
-        return f'{self.child.to_latex()}|{parents}'
-
-    def given(self, parents: XList[Variable]) -> ConditionalProbability:
-        """Create a new conditional distribution with this distribution's children, parents, and the given parent(s).
-
-        :param parents: A variable or list of variables to include as conditions in the new conditional distribution,
-            in addition to the variables already in this conditional distribution
-        :returns: A new conditional probability distribution
+        :param parents: The variable(s) with which this distribution's parents are extended
+        :returns: A new distribution
+        :raises TypeError: If a distribution is given as the parents that contains conditionals
 
         .. note:: This function can be accessed with the or | operator.
         """
-        return ConditionalProbability(
-            child=self.child,
-            parents=[*self.parents, *_upgrade_variables(parents)],
-        )
-
-    def __or__(self, parents: XList[Variable]) -> ConditionalProbability:
+        if not isinstance(parents, Distribution):
+            return Distribution(
+                children=self.children,
+                parents=[*self.parents, *_upgrade_variables(parents)],
+            )
+        elif parents.is_conditioned():
+            raise TypeError('can not be given a distribution that has conditionals')
+        else:
+            # The parents variable is actually a Distribution instance with no parents,
+            #  so its children get appended as parents for the new mixed distribution
+            return Distribution(
+                children=self.children,
+                parents=[*self.parents, *parents.children],  # don't think about this too hard
+            )
+
+    def __or__(self, parents: XList[Variable]) -> Distribution:
         return self.given(parents)
 
 
 class Expression(_Mathable, ABC):
     """The abstract class representing all expressions."""
 
-    def _repr_latex_(self) -> str:  # hack for auto-display of latex in jupyter notebook
-        return f'${self.to_latex()}$'
-
+    @abstractmethod
     def __mul__(self, other):
-        raise NotImplementedError
+        pass
 
+    @abstractmethod
     def __truediv__(self, other):
-        raise NotImplementedError
+        pass
 
 
 class Probability(Expression):
@@ -294,32 +326,36 @@ class Probability(Expression):
 
     def __init__(
         self,
-        probability: Union[Variable, List[Variable], ConditionalProbability, JointProbability],
+        distribution: Union[Variable, List[Variable], Distribution],
         *args: Variable,
     ) -> None:
         """Create a probability expression over the given variable(s) or distribution.
 
-        :param probability: If given a :class:`ConditionalProbability` or :class:`JointProbability`,
-            creates a probability expression directly over the distribution. If given variable or
-            list of variables, conveniently creates a :class:`JointProbability` over the variable(s)
-            first.
-        :param args: If the first argument (``probability``) was given as a single variable, the
-            ``args`` variadic argument can be used to specify a list of additiona variables.
+        :param distribution: If given a :class:`Distribution`, creates a probability expression
+            directly over the distribution. If given variable or list of variables, conveniently
+            creates a :class:`Distribtion` with the variable(s) as children.
+        :param args: If the first argument (``distribution``) was given as a single variable, the
+            ``args`` variadic argument can be used to specify a list of additional variables.
         :raises ValueError: If varidic args are used incorrectly (i.e., in combination with a
-            list of variables, :class:`ConditionalProbability`, or :class:`JointProbability`.
+            list of variables or :class:`Distribution`.
 
         .. note:: This class is so commonly used, that it is aliased as :class:`P`.
 
-        Creation with a :class:`ConditionalProbability`:
+        Creation with a conditional distribution:
 
         >>> from y0.dsl import P, A, B
         >>> P(A | B)
 
-        Creation with a :class:`JointProbability`:
+        Creation with a joint distribution:
 
         >>> from y0.dsl import P, A, B
         >>> P(A & B)
 
+        Creation with a mixed joint/conditional distribution:
+
+        >>> from y0.dsl import P, A, B, C
+        >>> P(A & B | C)
+
         Creation with a single :class:`Variable`:
 
         >>> from y0.dsl import P, A
@@ -335,30 +371,30 @@ class Probability(Expression):
         >>> from y0.dsl import P, A, B
         >>> P(A, B)
         """
-        if isinstance(probability, Variable):
+        if isinstance(distribution, Variable):
             if not args:
-                probability = [probability]
+                distribution = [distribution]
             elif not all(isinstance(p, Variable) for p in args):
                 raise ValueError
             else:
-                probability = [probability, *args]
-        if isinstance(probability, list):
-            probability = JointProbability(probability)
-        self.probability = probability
+                distribution = [distribution, *args]
+        if isinstance(distribution, list):
+            distribution = Distribution(children=distribution)
+        self.distribution = distribution
 
     def to_text(self) -> str:
         """Output this probability in the internal string format."""
-        return f'P({self.probability.to_text()})'
+        return f'P({self.distribution.to_text()})'
 
     def to_latex(self) -> str:
         """Output this probability in the LaTeX string format."""
-        return f'P({self.probability.to_latex()})'
+        return f'P({self.distribution.to_latex()})'
 
     def __repr__(self):
-        return f'P({repr(self.probability)})'
+        return f'P({repr(self.distribution)})'
 
     def __eq__(self, other):
-        return isinstance(other, Probability) and self.probability == other.probability
+        return isinstance(other, Probability) and self.distribution == other.distribution
 
     def __mul__(self, other: Expression) -> Expression:
         if isinstance(other, Product):
diff --git a/src/y0/parser_utils.py b/src/y0/parser_utils.py
index f460b57..3d03bf4 100644
--- a/src/y0/parser_utils.py
+++ b/src/y0/parser_utils.py
@@ -4,9 +4,7 @@
 
 from pyparsing import Group, Optional, ParseResults, Suppress, Word, alphas, delimitedList
 
-from .dsl import (
-    ConditionalProbability, CounterfactualVariable, Intervention, JointProbability, Probability, Variable,
-)
+from .dsl import (CounterfactualVariable, Distribution, Intervention, Probability, Variable)
 
 __all__ = [
     'probability_pe',
@@ -47,13 +45,9 @@ def _make_variable(_s, _l, tokens: ParseResults) -> Variable:
 
 def _make_probability(_s, _l, tokens: ParseResults) -> Probability:
     children, parents = tokens['children'].asList(), tokens['parents'].asList()
-    if not parents:
-        return Probability(JointProbability(children=children))
     if not children:
         raise ValueError
-    if len(children) > 1:
-        raise ValueError
-    return Probability(ConditionalProbability(child=children[0], parents=parents))
+    return Probability(Distribution(children=children, parents=parents))
 
 
 # The suffix "pe" refers to :class:`pyparsing.ParserElement`, which is the

diff --git a/tests/test_dsl.py b/tests/test_dsl.py
index d7413c8..c3143c2 100644
--- a/tests/test_dsl.py
+++ b/tests/test_dsl.py
@@ -6,8 +6,8 @@ import itertools as itt
 import unittest
 
 from y0.dsl import (
-    A, B, C, ConditionalProbability, CounterfactualVariable, D, Fraction, Intervention, JointProbability, P, Q, S, Sum,
-    T, Variable, W, X, Y, Z,
+    A, B, C, CounterfactualVariable, D, Distribution, Fraction, Intervention, P, Q, S, Sum, T,
+    Variable, W, X, Y, Z,
 )
 
 V = Variable('V')
@@ -19,13 +19,18 @@ class TestDSL(unittest.TestCase):
     def assert_text(self, s: str, expression):
         """Assert the expression when it is converted to a string."""
         self.assertIsInstance(s, str)
-        self.assertEqual(s, expression.to_text())
+        self.assertEqual(s, expression.to_text(), msg=f'Expression: {repr(expression)}')
 
     def test_variable(self):
         """Test the variable DSL object."""
         self.assert_text('A', Variable('A'))
         self.assert_text('A', A)  # shorthand for testing purposes
 
+    def test_stop_the_madness(self):
+        """Test that a variable can not be named "P"."""
+        with self.assertRaises(ValueError):
+            _ = Variable('P')
+
     def test_intervention(self):
         """Test the invervention DSL object."""
         self.assert_text('W*', Intervention('W', True))
@@ -70,10 +75,10 @@ class TestDSL(unittest.TestCase):
             with self.subTest(a=a, b=b), self.assertRaises(ValueError):
                 Y @ Intervention('X', star=a) @ Intervention('X', star=b)
 
-    def test_conditional(self):
-        """Test the ConditionalProbability DSL object."""
+    def test_conditional_distribution(self):
+        """Test the :class:`Distribution` DSL object."""
         # Normal instantiation
-        self.assert_text('A|B', ConditionalProbability(A, [B]))
+        self.assert_text('A|B', Distribution(A, [B]))
 
         # Instantiation with list-based operand to or | operator
         self.assert_text('A|B', Variable('A') | [B])
@@ -97,29 +102,60 @@ class TestDSL(unittest.TestCase):
         self.assert_text('Y_{W,X*}|B,C', Y @ W @ ~X | B | C)
         self.assert_text('Y_{W,X*}|B_{Q*},C', Y @ W @ ~X | B @ Intervention('Q', True) | C)
 
-    def test_conditional_probability(self):
-        """Test generation of conditional probabilities."""
-        self.assert_text('P(A|B)', P(ConditionalProbability(A, [B])))
-        self.assert_text('P(A|B)', P(A | [B]))
-        self.assert_text('P(A|B,C)', P(ConditionalProbability(A, [B]) | C))
-        self.assert_text('P(A|B,C)', P(A | [B, C]))
-        self.assert_text('P(A|B,C)', P(A | B | C))
-
-    def test_joint(self):
+    def test_joint_distribution(self):
         """Test the JointProbability DSL object."""
-        self.assert_text('A,B', JointProbability([A, B]))
+        self.assert_text('A,B', Distribution([A, B]))
         self.assert_text('A,B', A & B)
-        self.assert_text('A,B,C', JointProbability([A, B, C]))
+        self.assert_text('A,B,C', Distribution([A, B, C]))
         self.assert_text('A,B,C', A & B & C)
 
-    def test_joint_probability(self):
-        """Test generation of joint probabilities."""
-        # Shortcut for list building
+    def test_probability(self):
+        """Test generation of probabilities."""
+        # Make sure there are children
+        with self.assertRaises(ValueError):
+            Distribution([])
+
+        # Test markov kernels (AKA has only one child variable)
+        self.assert_text('P(A|B)', P(Distribution(A, [B])))
+        self.assert_text('P(A|B)', P(A | [B]))
+        self.assert_text('P(A|B,C)', P(Distribution(A, [B]) | C))
+        self.assert_text('P(A|B,C)', P(A | [B, C]))
+        self.assert_text('P(A|B,C)', P(A | B | C))
+        self.assert_text('P(A|B,C)', P(A | B & C))
+
+        # Test simple joint distributions
         self.assert_text('P(A,B)', P([A, B]))
         self.assert_text('P(A,B)', P(A, B))
         self.assert_text('P(A,B)', P(A & B))
         self.assert_text('P(A,B,C)', P(A & B & C))
 
+        # Test mixed with single conditional
+        self.assert_text('P(A,B|C)', P(Distribution([A, B], [C])))
+        self.assert_text('P(A,B|C)', P(Distribution([A, B], C)))
+        self.assert_text('P(A,B|C)', P(Distribution([A, B]) | C))
+        self.assert_text('P(A,B|C)', P(A & B | C))
+
+        # Test mixed with multiple conditionals
+        self.assert_text('P(A,B|C,D)', P(Distribution([A, B], [C, D])))
+        self.assert_text('P(A,B|C,D)', P(Distribution([A, B]) | C | D))
+        self.assert_text('P(A,B|C,D)', P(Distribution([A, B], [C]) | D))
+        self.assert_text('P(A,B|C,D)', P(A & B | C | D))
+        self.assert_text('P(A,B|C,D)', P(A & B | [C, D]))
+        self.assert_text('P(A,B|C,D)', P(A & B | Distribution([C, D])))
+        self.assert_text('P(A,B|C,D)', P(A & B | C & D))
+
+    def test_conditioning_errors(self):
+        """Test erroring on conditionals."""
+        for expression in [
+            Distribution(B, C),
+            Distribution([B, C], D),
+            Distribution([B, C], [D, W]),
+        ]:
+            with self.assertRaises(TypeError):
+                _ = A | expression
+            with self.assertRaises(TypeError):
+                _ = X & Y | expression
+
     def test_sum(self):
         """Test the Sum DSL object."""
         # Sum with no variables

Unify joint and conditional probabilities
tests/test_dsl.py::TestDSL::test_conditional_distribution tests/test_dsl.py::TestDSL::test_conditioning_errors tests/test_dsl.py::TestDSL::test_counterfactual_errors tests/test_dsl.py::TestDSL::test_counterfactual_variable tests/test_dsl.py::TestDSL::test_intervention tests/test_dsl.py::TestDSL::test_jeremy tests/test_dsl.py::TestDSL::test_joint_distribution tests/test_dsl.py::TestDSL::test_probability tests/test_dsl.py::TestDSL::test_stop_the_madness tests/test_dsl.py::TestDSL::test_sum tests/test_dsl.py::TestDSL::test_variable