diff --git a/motile/costs/appear.py b/motile/costs/appear.py
index acac553..a0e36d8 100644
--- a/motile/costs/appear.py
+++ b/motile/costs/appear.py
@@ -15,15 +15,30 @@ class Appear(Costs):
 
     Args:
 
+        weight (float):
+            The weight to apply to the cost of each starting track.
+
+        attribute (string):
+            The name of the attribute to use to look up costs. Default is
+            ``None``, which means that a constant cost is used.
+
         constant (float):
             A constant cost for each node that starts a track.
     """
 
-    def __init__(self, constant: float) -> None:
+    def __init__(
+        self, weight: float = 1, attribute: str | None = None, constant: float = 0
+    ) -> None:
+        self.weight = Weight(weight)
         self.constant = Weight(constant)
+        self.attribute = attribute
 
     def apply(self, solver: Solver) -> None:
         appear_indicators = solver.get_variables(NodeAppear)
 
-        for index in appear_indicators.values():
+        for node, index in appear_indicators.items():
+            if self.attribute is not None:
+                solver.add_variable_cost(
+                    index, solver.graph.nodes[node][self.attribute], self.weight
+                )
             solver.add_variable_cost(index, 1.0, self.constant)
diff --git a/motile/costs/edge_distance.py b/motile/costs/edge_distance.py
index 733286e..6bb0cb7 100644
--- a/motile/costs/edge_distance.py
+++ b/motile/costs/edge_distance.py
@@ -24,13 +24,20 @@ class EdgeDistance(Costs):
 
         weight (float):
             The weight to apply to the distance to convert it into a cost.
+
+        constant (float):
+            A constant cost to add to all edges.
     """
 
     def __init__(
-        self, position_attributes: tuple[str, ...], weight: float = 1.0
+        self,
+        position_attributes: tuple[str, ...],
+        weight: float = 1.0,
+        constant: float = 0.0,
     ) -> None:
-        self.position_attributes = position_attributes
         self.weight = Weight(weight)
+        self.constant = Weight(constant)
+        self.position_attributes = position_attributes
 
     def apply(self, solver: Solver) -> None:
         edge_variables = solver.get_variables(EdgeSelected)
@@ -46,3 +53,4 @@ def apply(self, solver: Solver) -> None:
             feature = np.linalg.norm(pos_u - pos_v)
 
             solver.add_variable_cost(index, feature, self.weight)
+            solver.add_variable_cost(index, 1.0, self.constant)
diff --git a/motile/costs/split.py b/motile/costs/split.py
index f0332bc..d19aa06 100644
--- a/motile/costs/split.py
+++ b/motile/costs/split.py
@@ -14,17 +14,31 @@ class Split(Costs):
     """Costs for :class:`motile.variables.NodeSplit` variables.
 
     Args:
+        weight (float):
+            The weight to apply to the cost of each split.
+
+        attribute (string)
+            The name of the attribute to use to look up costs. Default is
+            ``None``, which means that a constant cost is used.
 
         constant (float):
             A constant cost for each node that has more than one selected
             child.
     """
 
-    def __init__(self, constant: float) -> None:
+    def __init__(
+        self, weight: float = 1, attribute: str | None = None, constant: float = 0
+    ) -> None:
+        self.weight = Weight(weight)
         self.constant = Weight(constant)
+        self.attribute = attribute
 
     def apply(self, solver: Solver) -> None:
         split_indicators = solver.get_variables(NodeSplit)
 
-        for index in split_indicators.values():
+        for node, index in split_indicators.items():
+            if self.attribute is not None:
+                solver.add_variable_cost(
+                    index, solver.graph.nodes[node][self.attribute], self.weight
+                )
             solver.add_variable_cost(index, 1.0, self.constant)
diff --git a/tests/test_api.py b/tests/test_api.py
index c1a5cea..e8f244f 100644
--- a/tests/test_api.py
+++ b/tests/test_api.py
@@ -1,8 +1,6 @@
-import unittest
-
 import motile
 from motile.constraints import MaxChildren, MaxParents
-from motile.costs import Appear, EdgeSelection, NodeSelection, Split
+from motile.costs import Appear, EdgeDistance, EdgeSelection, NodeSelection, Split
 from motile.data import (
     arlo_graph,
     arlo_graph_nx,
@@ -11,40 +9,44 @@
 )
 
 
-class TestAPI(unittest.TestCase):
-    def test_graph_creation_with_hyperedges(self):
-        graph = toy_hypergraph()
-        assert len(graph.nodes) == 7
-        assert len(graph.edges) == 10
+def test_graph_creation_with_hyperedges():
+    graph = toy_hypergraph()
+    assert len(graph.nodes) == 7
+    assert len(graph.edges) == 10
+
+
+def test_graph_creation_from_multiple_nx_graphs():
+    g1 = toy_hypergraph_nx()
+    g2 = arlo_graph_nx()
+    graph = motile.TrackGraph()
 
-    def test_graph_creation_from_multiple_nx_graphs(self):
-        g1 = toy_hypergraph_nx()
-        g2 = arlo_graph_nx()
-        graph = motile.TrackGraph()
+    graph.add_from_nx_graph(g1)
+    assert len(graph.nodes) == 7
+    assert len(graph.edges) == 10
+    assert graph.nodes[6]["x"] == 35
+    assert "prediction_distance" not in graph.edges[(0, 2)]
 
-        graph.add_from_nx_graph(g1)
-        assert len(graph.nodes) == 7
-        assert len(graph.edges) == 10
-        assert graph.nodes[6]["x"] == 35
-        assert "prediction_distance" not in graph.edges[(0, 2)]
+    graph.add_from_nx_graph(g2)
+    assert len(graph.nodes) == 7
+    assert len(graph.edges) == 11
+    assert graph.nodes[6]["x"] == 200
+    assert "prediction_distance" in graph.edges[(0, 2)]
 
-        graph.add_from_nx_graph(g2)
-        assert len(graph.nodes) == 7
-        assert len(graph.edges) == 11
-        assert graph.nodes[6]["x"] == 200
-        assert "prediction_distance" in graph.edges[(0, 2)]
 
-    def test_solver(self):
-        graph = arlo_graph()
+def test_solver():
+    graph = arlo_graph()
 
-        solver = motile.Solver(graph)
-        solver.add_costs(NodeSelection(weight=-1.0, attribute="score", constant=-100.0))
-        solver.add_costs(EdgeSelection(weight=1.0, attribute="prediction_distance"))
-        solver.add_costs(Appear(constant=200.0))
-        solver.add_costs(Split(constant=100.0))
-        solver.add_constraints(MaxParents(1))
-        solver.add_constraints(MaxChildren(2))
+    solver = motile.Solver(graph)
+    solver.add_costs(NodeSelection(weight=-1.0, attribute="score", constant=-100.0))
+    solver.add_costs(
+        EdgeSelection(weight=0.5, attribute="prediction_distance", constant=-1.0)
+    )
+    solver.add_costs(EdgeDistance(position_attributes=("x",), weight=0.5, constant=1.0))
+    solver.add_costs(Appear(constant=200.0, attribute="score", weight=-1.0))
+    solver.add_costs(Split(constant=100.0, attribute="score", weight=1.0))
+    solver.add_constraints(MaxParents(1))
+    solver.add_constraints(MaxChildren(2))
 
-        solution = solver.solve()
+    solution = solver.solve()
 
-        assert solution.get_value() == -200
+    assert solution.get_value() == -202