diff --git a/src/ert/analysis/_es_update.py b/src/ert/analysis/_es_update.py
index 4e1f8665b11..4d72c885246 100644
--- a/src/ert/analysis/_es_update.py
+++ b/src/ert/analysis/_es_update.py
@@ -423,7 +423,7 @@ def analysis_ES(
             Sigma_Y = np.diag(np.sqrt(np.diag(C_YY)))
             batch_size = 1000
             for parameter in update_step.parameters:
-                num_params = len(parameter)
+                num_params = temp_storage[parameter.name].shape[0]
                 correlation_threshold = module.localization_correlation_threshold(
                     ensemble_size
                 )
@@ -438,14 +438,9 @@ def analysis_ES(
                 for param_batch_idx in tqdm(batches):
                     X_local = temp_storage[parameter.name][param_batch_idx, :]
                     A = X_local - X_local.mean(axis=1, keepdims=True)
-                    # A_prime = A[param_batch_idx, :] - A[param_batch_idx, :].mean(
-                    #     axis=1, keepdims=True
-                    # )
-                    # C_AA = A_prime @ A_prime.T / (ensemble_size - 1)
                     C_AA = A @ A.T / (ensemble_size - 1)
 
                     # State-measurement covariance matrix
-                    # C_AY = A_prime @ Y_prime.T / (ensemble_size - 1)
                     C_AY = A @ Y_prime.T / (ensemble_size - 1)
                     Sigma_A = np.diag(np.sqrt(np.diag(C_AA)))
 
@@ -454,6 +449,10 @@ def analysis_ES(
                         np.linalg.inv(Sigma_A) @ C_AY @ np.linalg.inv(Sigma_Y)
                     )
                     c_bool = c_AY > correlation_threshold
+                    # Some parameters might be significantly correlated to the exact same
+                    # responses, making up what we cann a parameter group.
+                    # We want to call the update only once per such parameter group
+                    # to speed up computation.
                     param_groups = np.unique(c_bool, axis=0)
 
                     for grp in param_groups:
@@ -475,10 +474,9 @@ def analysis_ES(
                                 inversion=ies.InversionType(module.inversion),
                                 param_ensemble=param_ensemble,
                             )
-                            # A[param_batch_idx[param_idx], :] = smoother.update(A_chunk)
                             temp_storage[parameter.name][
                                 param_batch_idx[param_idx], :
-                            ] = smoother.udpate(X_chunk)
+                            ] = smoother.update(X_chunk)
         else:
             for parameter in update_step.parameters:
                 smoother.fit(
diff --git a/test-data/poly_example/poly_loc.ert b/test-data/poly_example/poly_loc.ert
new file mode 100644
index 00000000000..d0348521e89
--- /dev/null
+++ b/test-data/poly_example/poly_loc.ert
@@ -0,0 +1,22 @@
+JOBNAME poly_%d
+
+RANDOM_SEED 1234
+
+QUEUE_SYSTEM LOCAL
+QUEUE_OPTION LOCAL MAX_RUNNING 50
+
+RUNPATH runpath/es_loc/realization-<IENS>/iter-<ITER>
+
+ANALYSIS_SET_VAR STD_ENKF LOCALIZATION True
+
+OBS_CONFIG observations
+TIME_MAP time_map
+
+NUM_REALIZATIONS 100
+MIN_REALIZATIONS 1
+
+GEN_KW COEFFS coeff.tmpl coeffs.json coeff_priors
+GEN_DATA POLY_RES RESULT_FILE:poly_%d.out REPORT_STEPS:0 INPUT_FORMAT:ASCII
+
+INSTALL_JOB poly_eval POLY_EVAL
+SIMULATION_JOB poly_eval
diff --git a/test-data/poly_example/poly_loc_1.ert b/test-data/poly_example/poly_loc_1.ert
new file mode 100644
index 00000000000..6936037b73b
--- /dev/null
+++ b/test-data/poly_example/poly_loc_1.ert
@@ -0,0 +1,23 @@
+JOBNAME poly_%d
+
+RANDOM_SEED 1234
+
+QUEUE_SYSTEM LOCAL
+QUEUE_OPTION LOCAL MAX_RUNNING 50
+
+RUNPATH runpath/es_loc_1/realization-<IENS>/iter-<ITER>
+
+ANALYSIS_SET_VAR STD_ENKF LOCALIZATION True
+ANALYSIS_SET_VAR STD_ENKF LOCALIZATION_CORRELATION_THRESHOLD 1.0
+
+OBS_CONFIG observations
+TIME_MAP time_map
+
+NUM_REALIZATIONS 100
+MIN_REALIZATIONS 1
+
+GEN_KW COEFFS coeff.tmpl coeffs.json coeff_priors
+GEN_DATA POLY_RES RESULT_FILE:poly_%d.out REPORT_STEPS:0 INPUT_FORMAT:ASCII
+
+INSTALL_JOB poly_eval POLY_EVAL
+SIMULATION_JOB poly_eval
diff --git a/test-data/poly_example/poly_no_loc.ert b/test-data/poly_example/poly_no_loc.ert
new file mode 100644
index 00000000000..884adfdaccf
--- /dev/null
+++ b/test-data/poly_example/poly_no_loc.ert
@@ -0,0 +1,20 @@
+JOBNAME poly_%d
+
+RANDOM_SEED 1234
+
+QUEUE_SYSTEM LOCAL
+QUEUE_OPTION LOCAL MAX_RUNNING 50
+
+RUNPATH runpath/es_no_loc/realization-<IENS>/iter-<ITER>
+
+OBS_CONFIG observations
+TIME_MAP time_map
+
+NUM_REALIZATIONS 100
+MIN_REALIZATIONS 1
+
+GEN_KW COEFFS coeff.tmpl coeffs.json coeff_priors
+GEN_DATA POLY_RES RESULT_FILE:poly_%d.out REPORT_STEPS:0 INPUT_FORMAT:ASCII
+
+INSTALL_JOB poly_eval POLY_EVAL
+SIMULATION_JOB poly_eval
diff --git a/test-data/poly_example/poly_zero_loc.ert b/test-data/poly_example/poly_zero_loc.ert
new file mode 100644
index 00000000000..9dcd57ddf70
--- /dev/null
+++ b/test-data/poly_example/poly_zero_loc.ert
@@ -0,0 +1,23 @@
+JOBNAME poly_%d
+
+RANDOM_SEED 1234
+
+QUEUE_SYSTEM LOCAL
+QUEUE_OPTION LOCAL MAX_RUNNING 50
+
+RUNPATH runpath/es_zero_loc/realization-<IENS>/iter-<ITER>
+
+ANALYSIS_SET_VAR STD_ENKF LOCALIZATION True
+ANALYSIS_SET_VAR STD_ENKF LOCALIZATION_CORRELATION_THRESHOLD 0.0
+
+OBS_CONFIG observations
+TIME_MAP time_map
+
+NUM_REALIZATIONS 100
+MIN_REALIZATIONS 1
+
+GEN_KW COEFFS coeff.tmpl coeffs.json coeff_priors
+GEN_DATA POLY_RES RESULT_FILE:poly_%d.out REPORT_STEPS:0 INPUT_FORMAT:ASCII
+
+INSTALL_JOB poly_eval POLY_EVAL
+SIMULATION_JOB poly_eval
diff --git a/test-data/poly_example/test_localization.sh b/test-data/poly_example/test_localization.sh
new file mode 100644
index 00000000000..3f04a258692
--- /dev/null
+++ b/test-data/poly_example/test_localization.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+
+ert ensemble_smoother poly_no_loc.ert --target ES_no_loc
+
+ert ensemble_smoother poly_zero_loc.ert --target ES_zero_loc
+
+ert ensemble_smoother poly_loc.ert --target ES_loc
+
+ert ensemble_smoother poly_loc_1.ert --target ES_loc_1