diff --git a/test/data_for_test.py b/test/data_for_test.py
index 28b1a9a53eb52edfaf3ac7741b5f8e6d617b1ea8..483d50b65f311b8cabea7497b1b1626590b62032 100644
--- a/test/data_for_test.py
+++ b/test/data_for_test.py
@@ -31,16 +31,11 @@ class WindowData:
     ndim = ref.gas.ndim
     dirs = ref.gas.dirs
 
-    def __init__(self, states_str, direction, window_metrics):
+    def __init__(self, states, direction, window_metrics):
         self.direction = self.dirs[direction]
         self.dir_internal = self.direction-1
 
-        # FIXME: Move array_from_string stuff outside WindowResults
-        #   -- just pass an array & have external utilities that generate
-        #   Riemann, sine wave, etc. initial conditions
-        self.state_pair = u.transposed_array_from_string(states_str)
-        self.states = u.expand_to_n(self.state_pair, 6)
-
+        self.states = states
         self.metrics, self.jacobians = window_metrics
 
         self.fluxes = ref.pointwise_fluxes(self.states)
@@ -50,6 +45,23 @@ class WindowData:
                 )[:,:,self.dir_internal].T.copy(order="F")
 
 
+@pytest.fixture(scope="session")
+def states_generator():
+    def states(states_str):
+        if states_str == "sine":
+            rho = np.sin(0.01*np.arange(6)+1.55)
+            vel = np.repeat(np.array([1.0, 2.0, 3.0])[None,:], 6, axis=0)
+            pressure = np.repeat(3.2, 6)
+            return u.transposed_array([ref.gas.conserved(r, v, p)
+                for r, v, p
+                in zip(rho, vel, pressure)])
+        else:
+            state_pair = u.transposed_array_from_string(states_str)
+            return u.expand_to_n(state_pair, 6)
+
+    return states
+
+
 @pytest.fixture(scope="session")
 def metrics_generator():
     ndim = ref.gas.ndim
@@ -68,6 +80,9 @@ def metrics_generator():
 
 
 @pytest.fixture(scope="session", params=[
+    ("sine", "x", "uniform"),
+    ("sine", "y", "uniform"),
+    ("sine", "z", "uniform"),
     ("1 1 1 1 5.5,1 1 1 1 5.5", "x", "uniform"),
     ("1 1 1 1 5.5,1 1 1 1 5.5", "y", "uniform"),
     ("1 1 1 1 5.5,1 1 1 1 5.5", "z", "uniform"),
@@ -84,12 +99,14 @@ def metrics_generator():
     ("1 -2 -3 -1 11,2 -8 -12 -4 64", "y", "uniform"),
     ("1 -3 -1 -2 11,2 -12 -4 -8 64", "z", "uniform")
     ])
-def window_data(request, metrics_generator):
+def window_data(request, states_generator, metrics_generator):
     states_str = request.param[0]
     dir_str = request.param[1]
     metric_str = request.param[2]
 
-    return WindowData(states_str, dir_str, metrics_generator(metric_str))
+    return WindowData(states_generator(states_str),
+                      dir_str,
+                      metrics_generator(metric_str))
 
 
 class PairData:
diff --git a/test/ideal_gas.py b/test/ideal_gas.py
index 0be569fef27f36ab0a3dbc5ec0b15033a84eea09..85aa4b737a985ef7c0b83d1cec7fa9c9ca59d41a 100644
--- a/test/ideal_gas.py
+++ b/test/ideal_gas.py
@@ -47,13 +47,12 @@ def energy(state):
     return state[ndim+1]
 
 
-def kinetic_energy(state):
-    vel = velocity(state)
-    return 0.5*rho(state)*np.dot(vel, vel)
+def kinetic_energy(rho, vel):
+    return 0.5*rho*np.dot(vel, vel)
 
 
 def internal_energy(state):
-    return energy(state) - kinetic_energy(state)
+    return energy(state) - kinetic_energy(rho(state), velocity(state))
 
 
 def pressure(state):
@@ -75,3 +74,14 @@ def flux(state):
         result[ndim+1,i] += vel[i]*p
 
     return result
+
+
+def conserved(rho, vel, p):
+    def energy(rho, vel, p):
+        return p/(gamma - 1) + kinetic_energy(rho, vel)
+
+    state = np.empty(nvars)
+    state[0] = rho
+    state[1:nvars-1] = rho*vel
+    state[nvars-1] = energy(rho, vel, p)
+    return state
diff --git a/test/test_eigensystem.py b/test/test_eigensystem.py
index e7b64f151cdf397abe309f277883d3d4b0c2ec28..8c1ba9369290ae16a5245a886c6c64af49874b01 100644
--- a/test/test_eigensystem.py
+++ b/test/test_eigensystem.py
@@ -35,7 +35,8 @@ import pytest
 
 import utilities as u
 import weno_reference_implementation as ref
-from data_for_test import pair_data, window_data, metrics_generator
+from data_for_test import (
+        pair_data, window_data, states_generator, metrics_generator)
 
 
 def test_roe_uniform_grid_ideal_gas(queue, pair_data):
diff --git a/test/test_flux_window_ops.py b/test/test_flux_window_ops.py
index e6f0667db08b4e94999530440d4ef96f18ef83a2..4bdb27ec925db6dda7cb451d36c812c528b3a4f4 100644
--- a/test/test_flux_window_ops.py
+++ b/test/test_flux_window_ops.py
@@ -35,7 +35,8 @@ import pytest
 
 import utilities as u
 import weno_reference_implementation as ref
-from data_for_test import PairData, window_data, metrics_generator
+from data_for_test import (
+        PairData, window_data, states_generator, metrics_generator)
 
 
 class WindowResults: