diff --git a/examples/compressible/dcmip_3_1_meanflow_quads.py b/examples/compressible/dcmip_3_1_meanflow_quads.py
index 82611ef04..c96bbe9ff 100644
--- a/examples/compressible/dcmip_3_1_meanflow_quads.py
+++ b/examples/compressible/dcmip_3_1_meanflow_quads.py
@@ -84,7 +84,7 @@
 io = IO(domain, output, diagnostic_fields=diagnostic_fields)
 
 # Transport schemes
-transported_fields = [ImplicitMidpoint(domain, "u"),
+transported_fields = [TrapeziumRule(domain, "u"),
                       SSPRK3(domain, "rho", subcycles=2),
                       SSPRK3(domain, "theta", options=SUPGOptions(), subcycles=2)]
 transport_methods = [DGUpwind(eqns, field) for field in ["u", "rho", "theta"]]
diff --git a/examples/compressible/moist_bryan_fritsch.py b/examples/compressible/moist_bryan_fritsch.py
index 41f9930a9..c00191dad 100644
--- a/examples/compressible/moist_bryan_fritsch.py
+++ b/examples/compressible/moist_bryan_fritsch.py
@@ -62,7 +62,7 @@
                       SSPRK3(domain, "theta", options=EmbeddedDGOptions()),
                       SSPRK3(domain, "water_vapour", options=EmbeddedDGOptions()),
                       SSPRK3(domain, "cloud_water", options=EmbeddedDGOptions()),
-                      ImplicitMidpoint(domain, "u")]
+                      TrapeziumRule(domain, "u")]
 
 transport_methods = [DGUpwind(eqns, field) for field in ["u", "rho", "theta", "water_vapour", "cloud_water"]]
 
diff --git a/examples/compressible/mountain_hydrostatic.py b/examples/compressible/mountain_hydrostatic.py
index a57b2c530..b0bd8a76f 100644
--- a/examples/compressible/mountain_hydrostatic.py
+++ b/examples/compressible/mountain_hydrostatic.py
@@ -71,7 +71,7 @@
 
 # Transport schemes
 theta_opts = SUPGOptions()
-transported_fields = [ImplicitMidpoint(domain, "u"),
+transported_fields = [TrapeziumRule(domain, "u"),
                       SSPRK3(domain, "rho"),
                       SSPRK3(domain, "theta", options=theta_opts)]
 transport_methods = [DGUpwind(eqns, "u"),
diff --git a/examples/compressible/mountain_nonhydrostatic.py b/examples/compressible/mountain_nonhydrostatic.py
index 890f95ba2..47ad15d2f 100644
--- a/examples/compressible/mountain_nonhydrostatic.py
+++ b/examples/compressible/mountain_nonhydrostatic.py
@@ -70,7 +70,7 @@
 
 # Transport schemes
 theta_opts = SUPGOptions()
-transported_fields = [ImplicitMidpoint(domain, "u"),
+transported_fields = [TrapeziumRule(domain, "u"),
                       SSPRK3(domain, "rho"),
                       SSPRK3(domain, "theta", options=theta_opts)]
 transport_methods = [DGUpwind(eqns, "u"),
diff --git a/examples/compressible/robert_bubble.py b/examples/compressible/robert_bubble.py
index b89f6aa33..3e771f60e 100644
--- a/examples/compressible/robert_bubble.py
+++ b/examples/compressible/robert_bubble.py
@@ -52,7 +52,7 @@
 
 # Transport schemes
 theta_opts = EmbeddedDGOptions()
-transported_fields = [ImplicitMidpoint(domain, "u"),
+transported_fields = [TrapeziumRule(domain, "u"),
                       SSPRK3(domain, "rho"),
                       SSPRK3(domain, "theta", options=theta_opts)]
 
diff --git a/examples/compressible/skamarock_klemp_hydrostatic.py b/examples/compressible/skamarock_klemp_hydrostatic.py
index bfdaf4107..42d111f1e 100644
--- a/examples/compressible/skamarock_klemp_hydrostatic.py
+++ b/examples/compressible/skamarock_klemp_hydrostatic.py
@@ -56,7 +56,7 @@
 
 # Transport schemes
 theta_opts = SUPGOptions()
-transported_fields = [ImplicitMidpoint(domain, "u"),
+transported_fields = [TrapeziumRule(domain, "u"),
                       SSPRK3(domain, "rho"),
                       SSPRK3(domain, "theta", options=theta_opts)]
 
diff --git a/examples/compressible/skamarock_klemp_nonlinear.py b/examples/compressible/skamarock_klemp_nonlinear.py
index e84c01d64..2b544e043 100644
--- a/examples/compressible/skamarock_klemp_nonlinear.py
+++ b/examples/compressible/skamarock_klemp_nonlinear.py
@@ -64,7 +64,7 @@
 
 # Transport schemes
 theta_opts = SUPGOptions()
-transported_fields = [ImplicitMidpoint(domain, "u"),
+transported_fields = [TrapeziumRule(domain, "u"),
                       SSPRK3(domain, "rho"),
                       SSPRK3(domain, "theta", options=theta_opts)]
 transport_methods = [DGUpwind(eqns, "u"),
diff --git a/examples/compressible/straka_bubble.py b/examples/compressible/straka_bubble.py
index cbe32800d..20442bf44 100644
--- a/examples/compressible/straka_bubble.py
+++ b/examples/compressible/straka_bubble.py
@@ -62,7 +62,7 @@
 
     # Transport schemes
     theta_opts = SUPGOptions()
-    transported_fields = [ImplicitMidpoint(domain, "u"),
+    transported_fields = [TrapeziumRule(domain, "u"),
                           SSPRK3(domain, "rho"),
                           SSPRK3(domain, "theta", options=theta_opts)]
     transport_methods = [DGUpwind(eqns, "u"),
diff --git a/examples/incompressible/skamarock_klemp_incompressible.py b/examples/incompressible/skamarock_klemp_incompressible.py
index 26efb5f52..ce38a5230 100644
--- a/examples/incompressible/skamarock_klemp_incompressible.py
+++ b/examples/incompressible/skamarock_klemp_incompressible.py
@@ -54,7 +54,7 @@
 
 # Transport schemes
 b_opts = SUPGOptions()
-transported_fields = [ImplicitMidpoint(domain, "u"),
+transported_fields = [TrapeziumRule(domain, "u"),
                       SSPRK3(domain, "b", options=b_opts)]
 transport_methods = [DGUpwind(eqns, "u"), DGUpwind(eqns, "b", ibp=b_opts.ibp)]
 
diff --git a/examples/shallow_water/williamson_2.py b/examples/shallow_water/williamson_2.py
index 1c2a8f8ec..432dd7cc6 100644
--- a/examples/shallow_water/williamson_2.py
+++ b/examples/shallow_water/williamson_2.py
@@ -66,7 +66,7 @@
     io = IO(domain, output, diagnostic_fields=diagnostic_fields)
 
     # Transport schemes
-    transported_fields = [ImplicitMidpoint(domain, "u"),
+    transported_fields = [TrapeziumRule(domain, "u"),
                           SSPRK3(domain, "D", subcycles=2)]
     transport_methods = [DGUpwind(eqns, "u"), DGUpwind(eqns, "D")]
 
diff --git a/examples/shallow_water/williamson_5.py b/examples/shallow_water/williamson_5.py
index bb6b5d9b3..0bcb43a3d 100644
--- a/examples/shallow_water/williamson_5.py
+++ b/examples/shallow_water/williamson_5.py
@@ -70,7 +70,7 @@
     io = IO(domain, output, diagnostic_fields=diagnostic_fields)
 
     # Transport schemes
-    transported_fields = [ImplicitMidpoint(domain, "u"),
+    transported_fields = [TrapeziumRule(domain, "u"),
                           SSPRK3(domain, "D")]
     transport_methods = [DGUpwind(eqns, "u"), DGUpwind(eqns, "D")]
 
diff --git a/gusto/time_discretisation.py b/gusto/time_discretisation.py
index a4db0a168..f535dddee 100644
--- a/gusto/time_discretisation.py
+++ b/gusto/time_discretisation.py
@@ -18,7 +18,7 @@
 
 
 __all__ = ["ForwardEuler", "BackwardEuler", "SSPRK3", "RK4", "Heun",
-           "ThetaMethod", "ImplicitMidpoint", "BDF2", "TR_BDF2", "Leapfrog", "AdamsMoulton", "AdamsBashforth"]
+           "ThetaMethod", "TrapeziumRule", "BDF2", "TR_BDF2", "Leapfrog", "AdamsMoulton", "AdamsBashforth"]
 
 
 def wrapper_apply(original_apply):
@@ -634,23 +634,24 @@ def apply(self, x_out, x_in):
 
 class ThetaMethod(TimeDiscretisation):
     """
-    Implements the theta implicit-explicit timestepping method.
+    Implements the theta implicit-explicit timestepping method, which can
+    be thought as a generalised trapezium rule.
 
     The theta implicit-explicit timestepping method for operator F is written as
     y^(n+1) = y^n + dt*(1-theta)*F[y^n] + dt*theta*F[y^(n+1)]
     for off-centring parameter theta.
     """
 
-    def __init__(self, domain, field_name=None, theta=None,
+    def __init__(self, domain, theta, field_name=None,
                  solver_parameters=None, options=None):
         """
         Args:
             domain (:class:`Domain`): the model's domain object, containing the
                 mesh and the compatible function spaces.
+            theta (float): the off-centring parameter. theta = 1
+                corresponds to a backward Euler method. Defaults to None.
             field_name (str, optional): name of the field to be evolved.
                 Defaults to None.
-            theta (float, optional): the off-centring parameter. theta = 1
-                corresponds to a backward Euler method. Defaults to None.
             solver_parameters (dict, optional): dictionary of parameters to
                 pass to the underlying solver. Defaults to None.
             options (:class:`AdvectionOptions`, optional): an object containing
@@ -661,9 +662,7 @@ def __init__(self, domain, field_name=None, theta=None,
         Raises:
             ValueError: if theta is not provided.
         """
-        # TODO: would this be better as a non-optional argument? Or should the
-        # check be on the provided value?
-        if theta is None:
+        if (theta < 0 or theta > 1):
             raise ValueError("please provide a value for theta between 0 and 1")
         if isinstance(options, (EmbeddedDGOptions, RecoveryOptions)):
             raise NotImplementedError("Only SUPG advection options have been implemented for this time discretisation")
@@ -715,11 +714,12 @@ def apply(self, x_out, x_in):
         x_out.assign(self.x_out)
 
 
-class ImplicitMidpoint(ThetaMethod):
+class TrapeziumRule(ThetaMethod):
     """
-    Implements the implicit midpoint timestepping method.
+    Implements the trapezium rule timestepping method, also commonly known as
+    Crank Nicholson.
 
-    The implicit midpoint timestepping method for operator F is written as
+    The trapezium rule timestepping method for operator F is written as
     y^(n+1) = y^n + dt/2*F[y^n] + dt/2*F[y^(n+1)].
     It is equivalent to the "theta" method with theta = 1/2.
     """
@@ -739,7 +739,7 @@ def __init__(self, domain, field_name=None, solver_parameters=None,
                 to control the "wrapper" methods, such as Embedded DG or a
                 recovery method. Defaults to None.
         """
-        super().__init__(domain, field_name, theta=0.5,
+        super().__init__(domain, 0.5, field_name,
                          solver_parameters=solver_parameters,
                          options=options)
 
diff --git a/integration-tests/balance/test_compressible_balance.py b/integration-tests/balance/test_compressible_balance.py
index 03ecc285b..a9726dd5a 100644
--- a/integration-tests/balance/test_compressible_balance.py
+++ b/integration-tests/balance/test_compressible_balance.py
@@ -39,7 +39,7 @@ def setup_balance(dirname):
     io = IO(domain, output)
 
     # Set up transport schemes
-    transported_fields = [ImplicitMidpoint(domain, "u"),
+    transported_fields = [TrapeziumRule(domain, "u"),
                           SSPRK3(domain, "rho"),
                           SSPRK3(domain, "theta", options=EmbeddedDGOptions())]
     transport_methods = [DGUpwind(eqns, 'u'),
diff --git a/integration-tests/balance/test_saturated_balance.py b/integration-tests/balance/test_saturated_balance.py
index 59b16fe3e..2c89da089 100644
--- a/integration-tests/balance/test_saturated_balance.py
+++ b/integration-tests/balance/test_saturated_balance.py
@@ -82,7 +82,7 @@ def setup_saturated(dirname, recovered):
     if recovered:
         transported_fields.append(SSPRK3(domain, 'u', options=u_opts))
     else:
-        transported_fields.append(ImplicitMidpoint(domain, 'u'))
+        transported_fields.append(TrapeziumRule(domain, 'u'))
 
     transport_methods = [DGUpwind(eqns, 'u'),
                          DGUpwind(eqns, 'rho'),
diff --git a/integration-tests/balance/test_unsaturated_balance.py b/integration-tests/balance/test_unsaturated_balance.py
index 6f29f8c9d..c6e3f33a9 100644
--- a/integration-tests/balance/test_unsaturated_balance.py
+++ b/integration-tests/balance/test_unsaturated_balance.py
@@ -77,7 +77,7 @@ def setup_unsaturated(dirname, recovered):
     if recovered:
         transported_fields.append(SSPRK3(domain, "u", options=u_opts))
     else:
-        transported_fields.append(ImplicitMidpoint(domain, "u"))
+        transported_fields.append(TrapeziumRule(domain, "u"))
 
     transport_methods = [DGUpwind(eqns, 'u'),
                          DGUpwind(eqns, 'rho'),
diff --git a/integration-tests/equations/test_dry_compressible.py b/integration-tests/equations/test_dry_compressible.py
index 53377335a..2e293e474 100644
--- a/integration-tests/equations/test_dry_compressible.py
+++ b/integration-tests/equations/test_dry_compressible.py
@@ -39,7 +39,7 @@ def run_dry_compressible(tmpdir):
     io = IO(domain, output)
 
     # Transport schemes
-    transported_fields = [ImplicitMidpoint(domain, "u"),
+    transported_fields = [TrapeziumRule(domain, "u"),
                           SSPRK3(domain, "rho"),
                           SSPRK3(domain, "theta")]
     transport_methods = [DGUpwind(eqn, 'u'),
diff --git a/integration-tests/equations/test_incompressible.py b/integration-tests/equations/test_incompressible.py
index 12260d1c9..a3ac3d8d0 100644
--- a/integration-tests/equations/test_incompressible.py
+++ b/integration-tests/equations/test_incompressible.py
@@ -39,7 +39,7 @@ def run_incompressible(tmpdir):
 
     # Transport Schemes
     b_opts = SUPGOptions()
-    transported_fields = [ImplicitMidpoint(domain, "u"),
+    transported_fields = [TrapeziumRule(domain, "u"),
                           SSPRK3(domain, "b", options=b_opts)]
     transport_methods = [DGUpwind(eqn, "u"),
                          DGUpwind(eqn, "b", ibp=b_opts.ibp)]
diff --git a/integration-tests/equations/test_moist_compressible.py b/integration-tests/equations/test_moist_compressible.py
index 222914334..e65a27157 100644
--- a/integration-tests/equations/test_moist_compressible.py
+++ b/integration-tests/equations/test_moist_compressible.py
@@ -40,7 +40,7 @@ def run_moist_compressible(tmpdir):
     io = IO(domain, output)
 
     # Transport schemes
-    transported_fields = [ImplicitMidpoint(domain, "u"),
+    transported_fields = [TrapeziumRule(domain, "u"),
                           SSPRK3(domain, "rho"),
                           SSPRK3(domain, "theta")]
     transport_methods = [DGUpwind(eqn, "u"),
diff --git a/integration-tests/equations/test_sw_fplane.py b/integration-tests/equations/test_sw_fplane.py
index b508ca43d..305f7c81d 100644
--- a/integration-tests/equations/test_sw_fplane.py
+++ b/integration-tests/equations/test_sw_fplane.py
@@ -36,7 +36,7 @@ def run_sw_fplane(tmpdir):
     io = IO(domain, output, diagnostic_fields=[CourantNumber()])
 
     # Transport schemes
-    transported_fields = [ImplicitMidpoint(domain, "u"),
+    transported_fields = [TrapeziumRule(domain, "u"),
                           SSPRK3(domain, "D")]
     transport_methods = [DGUpwind(eqns, "u"),
                          DGUpwind(eqns, "D")]
diff --git a/integration-tests/equations/test_sw_triangle.py b/integration-tests/equations/test_sw_triangle.py
index dd637e365..455595c31 100644
--- a/integration-tests/equations/test_sw_triangle.py
+++ b/integration-tests/equations/test_sw_triangle.py
@@ -156,7 +156,7 @@ def test_sw_setup(tmpdir, u_transport_option):
     domain, eqns, io = setup_sw(dirname, dt, u_transport_option)
 
     # Transport schemes
-    transported_fields = [ImplicitMidpoint(domain, "u"),
+    transported_fields = [TrapeziumRule(domain, "u"),
                           SSPRK3(domain, "D")]
 
     transport_methods = [DGUpwind(eqns, 'u'),
diff --git a/integration-tests/model/test_time_discretisation.py b/integration-tests/model/test_time_discretisation.py
index 1b1f04106..5be78c871 100644
--- a/integration-tests/model/test_time_discretisation.py
+++ b/integration-tests/model/test_time_discretisation.py
@@ -28,7 +28,7 @@ def test_time_discretisation(tmpdir, scheme, tracer_setup):
     if scheme == "ssprk":
         transport_scheme = SSPRK3(domain)
     elif scheme == "implicit_midpoint":
-        transport_scheme = ImplicitMidpoint(domain)
+        transport_scheme = TrapeziumRule(domain)
     elif scheme == "RK4":
         transport_scheme = RK4(domain)
     elif scheme == "Heun":
diff --git a/integration-tests/transport/test_supg_transport.py b/integration-tests/transport/test_supg_transport.py
index 30422d8e6..813308ec7 100644
--- a/integration-tests/transport/test_supg_transport.py
+++ b/integration-tests/transport/test_supg_transport.py
@@ -39,7 +39,7 @@ def test_supg_transport_scalar(tmpdir, equation_form, scheme, space,
     if scheme == "ssprk":
         transport_scheme = SSPRK3(domain, options=opts)
     elif scheme == "implicit_midpoint":
-        transport_scheme = ImplicitMidpoint(domain, options=opts)
+        transport_scheme = TrapeziumRule(domain, options=opts)
 
     transport_method = DGUpwind(eqn, "f", ibp=ibp)
     timestepper = PrescribedTransport(eqn, transport_scheme, setup.io, transport_method)
@@ -81,7 +81,7 @@ def test_supg_transport_vector(tmpdir, equation_form, scheme, space,
     if scheme == "ssprk":
         transport_scheme = SSPRK3(domain, options=opts)
     elif scheme == "implicit_midpoint":
-        transport_scheme = ImplicitMidpoint(domain, options=opts)
+        transport_scheme = TrapeziumRule(domain, options=opts)
 
     transport_method = DGUpwind(eqn, "f", ibp=ibp)
     timestepper = PrescribedTransport(eqn, transport_scheme, setup.io, transport_method)