diff --git a/docs/demos/tutorials/03_Blocking.ipynb b/docs/demos/tutorials/03_Blocking.ipynb
index 929a13490a..83e86a4418 100644
--- a/docs/demos/tutorials/03_Blocking.ipynb
+++ b/docs/demos/tutorials/03_Blocking.ipynb
@@ -153,19 +153,19 @@
     "\n",
     "blocking_rule_1 = block_on([\"substr(first_name, 1,1)\", \"surname\"])\n",
     "count = linker.count_num_comparisons_from_blocking_rule(blocking_rule_1)\n",
-    "print(f\"Number of comparisons generated by '{blocking_rule_1.sql}': {count:,.0f}\")\n",
+    "print(f\"Number of comparisons generated by '{blocking_rule_1.blocking_rule_sql}': {count:,.0f}\")\n",
     "\n",
     "blocking_rule_2 = block_on(\"surname\")\n",
     "count = linker.count_num_comparisons_from_blocking_rule(blocking_rule_2)\n",
-    "print(f\"Number of comparisons generated by '{blocking_rule_2.sql}': {count:,.0f}\")\n",
+    "print(f\"Number of comparisons generated by '{blocking_rule_2.blocking_rule_sql}': {count:,.0f}\")\n",
     "\n",
     "blocking_rule_3 = block_on(\"email\")\n",
     "count = linker.count_num_comparisons_from_blocking_rule(blocking_rule_3)\n",
-    "print(f\"Number of comparisons generated by '{blocking_rule_3.sql}': {count:,.0f}\")\n",
+    "print(f\"Number of comparisons generated by '{blocking_rule_3.blocking_rule_sql}': {count:,.0f}\")\n",
     "\n",
     "blocking_rule_4 = block_on([\"city\", \"first_name\"])\n",
     "count = linker.count_num_comparisons_from_blocking_rule(blocking_rule_4)\n",
-    "print(f\"Number of comparisons generated by '{blocking_rule_4.sql}': {count:,.0f}\")\n"
+    "print(f\"Number of comparisons generated by '{blocking_rule_4.blocking_rule_sql}': {count:,.0f}\")\n"
    ]
   },
   {
diff --git a/splink/accuracy.py b/splink/accuracy.py
index d2b140ff08..d8a92a0491 100644
--- a/splink/accuracy.py
+++ b/splink/accuracy.py
@@ -1,4 +1,5 @@
 from copy import deepcopy
+from typing import TYPE_CHECKING
 
 from .block_from_labels import block_from_labels
 from .blocking import BlockingRule
@@ -6,6 +7,9 @@
 from .predict import predict_from_comparison_vectors_sqls
 from .sql_transform import move_l_r_table_prefix_to_column_suffix
 
+if TYPE_CHECKING:
+    from .linker import Linker
+
 
 def truth_space_table_from_labels_with_predictions_sqls(
     threshold_actual=0.5, match_weight_round_to_nearest=None
@@ -143,10 +147,11 @@ def truth_space_table_from_labels_with_predictions_sqls(
     return sqls
 
 
-def _select_found_by_blocking_rules(linker):
+def _select_found_by_blocking_rules(linker: "Linker"):
     brs = linker._settings_obj._blocking_rules_to_generate_predictions
+
     if brs:
-        brs = [move_l_r_table_prefix_to_column_suffix(b.blocking_rule) for b in brs]
+        brs = [move_l_r_table_prefix_to_column_suffix(b.blocking_rule_sql) for b in brs]
         brs = [f"(coalesce({b}, false))" for b in brs]
         brs = " OR ".join(brs)
         br_col = f" ({brs}) "
diff --git a/splink/analyse_blocking.py b/splink/analyse_blocking.py
index d4105123a5..d2f70ecbe3 100644
--- a/splink/analyse_blocking.py
+++ b/splink/analyse_blocking.py
@@ -118,7 +118,7 @@ def cumulative_comparisons_generated_by_blocking_rules(
     for row, br in zip(br_count, brs_as_objs):
         out_dict = {
             "row_count": row,
-            "rule": br.blocking_rule,
+            "rule": br.blocking_rule_sql,
         }
         if output_chart:
             cumulative_sum += row
diff --git a/splink/blocking.py b/splink/blocking.py
index 40ed9a1c43..303a4c6622 100644
--- a/splink/blocking.py
+++ b/splink/blocking.py
@@ -3,7 +3,7 @@
 from sqlglot import parse_one
 from sqlglot.expressions import Join, Column
 from sqlglot.optimizer.eliminate_joins import join_condition
-from typing import TYPE_CHECKING, Union
+from typing import TYPE_CHECKING, List
 import logging
 
 from .misc import ensure_is_list
@@ -40,15 +40,20 @@ def blocking_rule_to_obj(br):
 class BlockingRule:
     def __init__(
         self,
-        blocking_rule: BlockingRule | dict | str,
+        blocking_rule_sql: str,
         salting_partitions=1,
         sqlglot_dialect: str = None,
     ):
         if sqlglot_dialect:
             self._sql_dialect = sqlglot_dialect
 
-        self.blocking_rule = blocking_rule
-        self.preceding_rules = []
+        # Temporarily just to see if tests still pass
+        if not isinstance(blocking_rule_sql, str):
+            raise ValueError(
+                f"Blocking rule must be a string, not {type(blocking_rule_sql)}"
+            )
+        self.blocking_rule_sql = blocking_rule_sql
+        self.preceding_rules: List[BlockingRule] = []
         self.sqlglot_dialect = sqlglot_dialect
         self.salting_partitions = salting_partitions
 
@@ -60,25 +65,30 @@ def sql_dialect(self):
     def match_key(self):
         return len(self.preceding_rules)
 
-    @property
-    def sql(self):
-        # Wrapper to reveal the underlying SQL
-        return self.blocking_rule
-
     def add_preceding_rules(self, rules):
         rules = ensure_is_list(rules)
         self.preceding_rules = rules
 
-    @property
-    def and_not_preceding_rules_sql(self):
-        if not self.preceding_rules:
-            return ""
+    def exclude_pairs_generated_by_this_rule_sql(self):
+        """A SQL string specifying how to exclude the results
+        of THIS blocking rule from subseqent blocking statements,
+        so that subsequent statements do not produce duplicate pairs
+        """
 
         # Note the coalesce function is important here - otherwise
         # you filter out any records with nulls in the previous rules
         # meaning these comparisons get lost
+        return f"coalesce(({self.blocking_rule_sql}),false)"
+
+    @property
+    def exclude_pairs_generated_by_all_preceding_rules_sql(self):
+        """A SQL string that excludes the results of ALL previous blocking rules from
+        the pairwise comparisons generated.
+        """
+        if not self.preceding_rules:
+            return ""
         or_clauses = [
-            f"coalesce(({r.blocking_rule}), false)" for r in self.preceding_rules
+            br.exclude_pairs_generated_by_this_rule_sql() for br in self.preceding_rules
         ]
         previous_rules = " OR ".join(or_clauses)
         return f"AND NOT ({previous_rules})"
@@ -86,14 +96,14 @@ def and_not_preceding_rules_sql(self):
     @property
     def salted_blocking_rules(self):
         if self.salting_partitions == 1:
-            yield self.blocking_rule
+            yield self.blocking_rule_sql
         else:
             for n in range(self.salting_partitions):
-                yield f"{self.blocking_rule} and ceiling(l.__splink_salt * {self.salting_partitions}) = {n+1}"  # noqa: E501
+                yield f"{self.blocking_rule_sql} and ceiling(l.__splink_salt * {self.salting_partitions}) = {n+1}"  # noqa: E501
 
     @property
     def _parsed_join_condition(self):
-        br = self.blocking_rule
+        br = self.blocking_rule_sql
         return parse_one("INNER JOIN r", into=Join).on(
             br, dialect=self.sqlglot_dialect
         )  # using sqlglot==11.4.1
@@ -147,7 +157,7 @@ def as_dict(self):
         "The minimal representation of the blocking rule"
         output = {}
 
-        output["blocking_rule"] = self.blocking_rule
+        output["blocking_rule"] = self.blocking_rule_sql
         output["sql_dialect"] = self.sql_dialect
 
         if self.salting_partitions > 1 and self.sql_dialect == "spark":
@@ -157,7 +167,7 @@ def as_dict(self):
 
     def _as_completed_dict(self):
         if not self.salting_partitions > 1 and self.sql_dialect == "spark":
-            return self.blocking_rule
+            return self.blocking_rule_sql
         else:
             return self.as_dict()
 
@@ -166,7 +176,7 @@ def descr(self):
         return "Custom" if not hasattr(self, "_description") else self._description
 
     def _abbreviated_sql(self, cutoff=75):
-        sql = self.blocking_rule
+        sql = self.blocking_rule_sql
         return (sql[:cutoff] + "...") if len(sql) > cutoff else sql
 
     def __repr__(self):
@@ -312,7 +322,7 @@ def block_using_rules_sqls(linker: Linker):
         if apply_salt:
             salted_blocking_rules = br.salted_blocking_rules
         else:
-            salted_blocking_rules = [br.blocking_rule]
+            salted_blocking_rules = [br.blocking_rule_sql]
 
         for salted_br in salted_blocking_rules:
             sql = f"""
@@ -324,7 +334,7 @@ def block_using_rules_sqls(linker: Linker):
             inner join {linker._input_tablename_r} as r
             on
             ({salted_br})
-            {br.and_not_preceding_rules_sql}
+            {br.exclude_pairs_generated_by_all_preceding_rules_sql}
             {where_condition}
             """
 
diff --git a/splink/blocking_rule_composition.py b/splink/blocking_rule_composition.py
index e6c4ce38f4..29cb01d9f6 100644
--- a/splink/blocking_rule_composition.py
+++ b/splink/blocking_rule_composition.py
@@ -295,7 +295,7 @@ def not_(*brls: BlockingRule | dict | str, salting_partitions: int = 1) -> Block
 
     brls, sql_dialect, salt = _parse_blocking_rules(*brls)
     br = brls[0]
-    blocking_rule = f"NOT ({br.blocking_rule})"
+    blocking_rule = f"NOT ({br.blocking_rule_sql})"
 
     return BlockingRule(
         blocking_rule,
@@ -314,9 +314,9 @@ def _br_merge(
 
     brs, sql_dialect, salt = _parse_blocking_rules(*brls)
     if len(brs) > 1:
-        conditions = (f"({br.blocking_rule})" for br in brs)
+        conditions = (f"({br.blocking_rule_sql})" for br in brs)
     else:
-        conditions = (br.blocking_rule for br in brs)
+        conditions = (br.blocking_rule_sql for br in brs)
 
     blocking_rule = f" {clause} ".join(conditions)
 
diff --git a/splink/em_training_session.py b/splink/em_training_session.py
index 4ed9706e90..aaf01c986e 100644
--- a/splink/em_training_session.py
+++ b/splink/em_training_session.py
@@ -135,7 +135,7 @@ def _training_log_message(self):
         else:
             mu = "m and u probabilities"
 
-        blocking_rule = self._blocking_rule_for_training.blocking_rule
+        blocking_rule = self._blocking_rule_for_training.blocking_rule_sql
 
         logger.info(
             f"Estimating the {mu} of the model by blocking on:\n"
@@ -176,7 +176,7 @@ def _train(self):
         # check that the blocking rule actually generates _some_ record pairs,
         # if not give the user a helpful message
         if not cvv.as_record_dict(limit=1):
-            br_sql = f"`{self._blocking_rule_for_training.blocking_rule}`"
+            br_sql = f"`{self._blocking_rule_for_training.blocking_rule_sql}`"
             raise EMTrainingException(
                 f"Training rule {br_sql} resulted in no record pairs.  "
                 "This means that in the supplied data set "
@@ -195,7 +195,7 @@ def _train(self):
         # in the original (main) setting object
         expectation_maximisation(self, cvv)
 
-        rule = self._blocking_rule_for_training.blocking_rule
+        rule = self._blocking_rule_for_training.blocking_rule_sql
         training_desc = f"EM, blocked on: {rule}"
 
         # Add m and u values to original settings
@@ -254,7 +254,7 @@ def _blocking_adjusted_probability_two_random_records_match(self):
         comp_levels = self._comparison_levels_to_reverse_blocking_rule
         if not comp_levels:
             comp_levels = self._original_settings_obj._get_comparison_levels_corresponding_to_training_blocking_rule(  # noqa
-                self._blocking_rule_for_training.blocking_rule
+                self._blocking_rule_for_training.blocking_rule_sql
             )
 
         for cl in comp_levels:
@@ -271,7 +271,7 @@ def _blocking_adjusted_probability_two_random_records_match(self):
         logger.log(
             15,
             f"\nProb two random records match adjusted for blocking on "
-            f"{self._blocking_rule_for_training.blocking_rule}: "
+            f"{self._blocking_rule_for_training.blocking_rule_sql}: "
             f"{adjusted_prop_m:.3f}",
         )
         return adjusted_prop_m
@@ -411,7 +411,7 @@ def __repr__(self):
                 for cc in self._comparisons_that_cannot_be_estimated
             ]
         )
-        blocking_rule = self._blocking_rule_for_training.blocking_rule
+        blocking_rule = self._blocking_rule_for_training.blocking_rule_sql
         return (
             f"<EMTrainingSession, blocking on {blocking_rule}, "
             f"deactivating comparisons {deactivated_cols}>"
diff --git a/splink/linker.py b/splink/linker.py
index 2c4e1080c9..c4a96b4a87 100644
--- a/splink/linker.py
+++ b/splink/linker.py
@@ -994,7 +994,7 @@ def _populate_probability_two_random_records_match_from_trained_values(self):
                 15,
                 "\n"
                 f"Probability two random records match from trained model blocking on "
-                f"{em_training_session._blocking_rule_for_training.blocking_rule}: "
+                f"{em_training_session._blocking_rule_for_training.blocking_rule_sql}: "
                 f"{training_lambda:,.3f}",
             )
 
@@ -1630,7 +1630,7 @@ def estimate_parameters_using_expectation_maximisation(
         self._initialise_df_concat_with_tf()
 
         # Extract the blocking rule
-        blocking_rule = blocking_rule_to_obj(blocking_rule).blocking_rule
+        blocking_rule = blocking_rule_to_obj(blocking_rule).blocking_rule_sql
 
         if comparisons_to_deactivate:
             # If user provided a string, convert to Comparison object
@@ -3100,7 +3100,7 @@ def count_num_comparisons_from_blocking_rule(
             int: The number of comparisons generated by the blocking rule
         """
 
-        blocking_rule = blocking_rule_to_obj(blocking_rule).blocking_rule
+        blocking_rule = blocking_rule_to_obj(blocking_rule).blocking_rule_sql
 
         sql = vertically_concatenate_sql(self)
         self._enqueue_sql(sql, "__splink__df_concat")
diff --git a/splink/settings.py b/splink/settings.py
index 90cc165dfc..f14b2d79c1 100644
--- a/splink/settings.py
+++ b/splink/settings.py
@@ -2,8 +2,9 @@
 
 import logging
 from copy import deepcopy
+from typing import List
 
-from .blocking import blocking_rule_to_obj
+from .blocking import BlockingRule, blocking_rule_to_obj
 from .charts import m_u_parameters_chart, match_weights_chart
 from .comparison import Comparison
 from .comparison_level import ComparisonLevel
@@ -125,7 +126,7 @@ def _get_additional_columns_to_retain(self):
             used_by_brs = []
             for br in self._blocking_rules_to_generate_predictions:
                 used_by_brs.extend(
-                    get_columns_used_from_sql(br.blocking_rule, br.sql_dialect)
+                    get_columns_used_from_sql(br.blocking_rule_sql, br.sql_dialect)
                 )
 
             used_by_brs = [InputColumn(c) for c in used_by_brs]
@@ -300,7 +301,7 @@ def _get_comparison_by_output_column_name(self, name):
                 return cc
         raise ValueError(f"No comparison column with name {name}")
 
-    def _brs_as_objs(self, brs_as_strings):
+    def _brs_as_objs(self, brs_as_strings) -> List[BlockingRule]:
         brs_as_objs = [blocking_rule_to_obj(br) for br in brs_as_strings]
         for n, br in enumerate(brs_as_objs):
             br.add_preceding_rules(brs_as_objs[:n])
diff --git a/splink/settings_validation/settings_validator.py b/splink/settings_validation/settings_validator.py
index 06e24acfb9..ca7fe754c0 100644
--- a/splink/settings_validation/settings_validator.py
+++ b/splink/settings_validation/settings_validator.py
@@ -4,6 +4,7 @@
 import re
 from functools import reduce
 from operator import and_
+from typing import List
 
 import sqlglot
 
@@ -49,9 +50,9 @@ def uid(self):
         return self.clean_list_of_column_names(uid_as_tree)
 
     @property
-    def blocking_rules(self):
+    def blocking_rules(self) -> List[str]:
         brs = self.settings_obj._blocking_rules_to_generate_predictions
-        return [br.blocking_rule for br in brs]
+        return [br.blocking_rule_sql for br in brs]
 
     @property
     def comparisons(self):
diff --git a/tests/test_blocking.py b/tests/test_blocking.py
index 0eb2113cc5..e84297ddc0 100644
--- a/tests/test_blocking.py
+++ b/tests/test_blocking.py
@@ -19,7 +19,7 @@ def test_binary_composition_internals_OR(test_helpers, dialect):
     assert br_surname.__repr__() == exp_txt.format("Exact match", em_rule)
     assert BlockingRule(em_rule).__repr__() == exp_txt.format("Custom", em_rule)
 
-    assert br_surname.blocking_rule == em_rule
+    assert br_surname.blocking_rule_sql == em_rule
     assert br_surname.salting_partitions == 4
     assert br_surname.preceding_rules == []
 
@@ -40,13 +40,13 @@ def test_binary_composition_internals_OR(test_helpers, dialect):
         brl.exact_match_rule("help4"),
     ]
     brs_as_objs = settings_tester._brs_as_objs(brs_as_strings)
-    brs_as_txt = [blocking_rule_to_obj(br).blocking_rule for br in brs_as_strings]
+    brs_as_txt = [blocking_rule_to_obj(br).blocking_rule_sql for br in brs_as_strings]
 
     assert brs_as_objs[0].preceding_rules == []
 
     def assess_preceding_rules(settings_brs_index):
         br_prec = brs_as_objs[settings_brs_index].preceding_rules
-        br_prec_txt = [br.blocking_rule for br in br_prec]
+        br_prec_txt = [br.blocking_rule_sql for br in br_prec]
         assert br_prec_txt == brs_as_txt[:settings_brs_index]
 
     assess_preceding_rules(1)
diff --git a/tests/test_blocking_rule_composition.py b/tests/test_blocking_rule_composition.py
index fadc9d26bd..3e02c89d5b 100644
--- a/tests/test_blocking_rule_composition.py
+++ b/tests/test_blocking_rule_composition.py
@@ -11,7 +11,7 @@ def binary_composition_internals(clause, comp_fun, brl, dialect):
     # Test what happens when only one value is fed
     # It should just report the regular outputs of our comparison level func
     level = comp_fun(brl.exact_match_rule("tom"))
-    assert level.blocking_rule == f"l.{q}tom{q} = r.{q}tom{q}"
+    assert level.blocking_rule_sql == f"l.{q}tom{q} = r.{q}tom{q}"
 
     # Exact match and null level composition
     level = comp_fun(
@@ -19,12 +19,12 @@ def binary_composition_internals(clause, comp_fun, brl, dialect):
         brl.exact_match_rule("surname"),
     )
     exact_match_sql = f"(l.{q}first_name{q} = r.{q}first_name{q}) {clause} (l.{q}surname{q} = r.{q}surname{q})"  # noqa: E501
-    assert level.blocking_rule == exact_match_sql
+    assert level.blocking_rule_sql == exact_match_sql
     # brl.not_(or_(...)) composition
     level = brl.not_(
         comp_fun(brl.exact_match_rule("first_name"), brl.exact_match_rule("surname")),
     )
-    assert level.blocking_rule == f"NOT ({exact_match_sql})"
+    assert level.blocking_rule_sql == f"NOT ({exact_match_sql})"
 
     # Check salting outputs
     # salting included in the composition function
diff --git a/tests/test_u_train.py b/tests/test_u_train.py
index 453e13beae..274701ebcd 100644
--- a/tests/test_u_train.py
+++ b/tests/test_u_train.py
@@ -39,7 +39,7 @@ def test_u_train(test_helpers, dialect):
     assert cl_no.u_probability == (denom - 2) / denom
 
     br = linker._settings_obj._blocking_rules_to_generate_predictions[0]
-    assert br.blocking_rule == "l.name = r.name"
+    assert br.blocking_rule_sql == "l.name = r.name"
 
 
 @mark_with_dialects_excluding()