diff --git a/crates/oq3_parser/src/grammar/expressions.rs b/crates/oq3_parser/src/grammar/expressions.rs
index 54c0a75..825fd23 100644
--- a/crates/oq3_parser/src/grammar/expressions.rs
+++ b/crates/oq3_parser/src/grammar/expressions.rs
@@ -223,13 +223,11 @@ fn current_op(p: &Parser<'_>) -> (u8, SyntaxKind, Associativity) {
         T![>]                  => (5,  T![>],   Left),
         T![=] if p.at(T![=>])  => NOT_AN_OP,
         T![=] if p.at(T![==])  => (5,  T![==],  Left),
-        // r-a had 1 as the bp here. But this attempts to parse
-        // `x + y = 3`; as `(x + y) = 3;` which is probably not what the user meant.
-        // Putting 12 as the bp instead of 1 parses this as
-        // `x + (y = 3)`. In OQ3, this is still illegal, but the user will get a more
-        // informative error message. That an assignment statement is not allowed here.
-        // This may have unintended consequences and we will need to replace the 12 with 1.
-        T![=]                  => (12,  T![=],   Right),
+        // Assignment has lower precedence than every value-producing binary
+        // operator, so `x = y ^ z` keeps the complete expression on the RHS.
+        // `expr_bp` separately checks that the completed LHS is an identifier
+        // or indexed identifier, rejecting forms such as `(x + y) = z`.
+        T![=]                  => (1,   T![=],   Right),
         T![<] if p.at(T![<=])  => (5,  T![<=],  Left),
         T![<] if p.at(T![<<=]) => (1,  T![<<=], Right),
         T![<] if p.at(T![<<])  => (9,  T![<<],  Left),
diff --git a/crates/oq3_syntax/src/tests.rs b/crates/oq3_syntax/src/tests.rs
index 9bb6ac8..4282864 100644
--- a/crates/oq3_syntax/src/tests.rs
+++ b/crates/oq3_syntax/src/tests.rs
@@ -325,3 +325,22 @@ z + int[32](x);
     let parse = SourceFile::parse(code);
     assert_eq!(parse.errors.len(), 0);
 }
+
+#[test]
+fn parse_assignment_rhs_test() {
+    let code = r##"
+bit a;
+bit b;
+bit c;
+a = b ^ c;
+    "##;
+    let parse = SourceFile::parse(code);
+    assert!(parse.ok().is_ok());
+}
+
+#[test]
+fn parse_assignment_invalid_lhs_test() {
+    let parse = SourceFile::parse("x + y = 3;");
+    assert_eq!(parse.errors.len(), 1);
+    assert_eq!(parse.errors[0].message(), "Illegal LHS in assignment");
+}
diff --git a/crates/pipeline-tests/tests/snapshots/runner__tests__snippets__invalid__statements__measure.qasm-parse.snap b/crates/pipeline-tests/tests/snapshots/runner__tests__snippets__invalid__statements__measure.qasm-parse.snap
index 69283ff..c183538 100644
--- a/crates/pipeline-tests/tests/snapshots/runner__tests__snippets__invalid__statements__measure.qasm-parse.snap
+++ b/crates/pipeline-tests/tests/snapshots/runner__tests__snippets__invalid__statements__measure.qasm-parse.snap
@@ -7,7 +7,7 @@ expect-parse: Diag
 --- parser ---
 ok: false
 panicked: false
-errors: 15
+errors: 12
 --- ast ---
 SOURCE_FILE@0..234: 
 measure $0, $1;
@@ -39,10 +39,9 @@ HARDWARE_QUBIT@34..36: $0
 ERROR@36..37: ,
 EXPR_STMT@38..41: $1;
 HARDWARE_QUBIT@38..40: $1
-EXPR_STMT@42..59: a = measure $0 ->
-BIN_EXPR@42..59: a = measure $0 ->
-ASSIGNMENT_STMT@42..56: a = measure $0
+ASSIGNMENT_STMT@42..59: a = measure $0 ->
 IDENTIFIER@42..43: a
+BIN_EXPR@46..59: measure $0 ->
 MEASURE_EXPRESSION@46..56: measure $0
 HARDWARE_QUBIT@54..56: $0
 ERROR@58..59: >
@@ -77,17 +76,15 @@ SCALAR_TYPE@126..132: bit[1]
 DESIGNATOR@129..132: [1]
 LITERAL@130..131: 1
 NAME@133..134: a
-EXPR_STMT@181..200: a = 2 * measure $0;
-BIN_EXPR@181..199: a = 2 * measure $0
-ASSIGNMENT_STMT@181..186: a = 2
+ASSIGNMENT_STMT@181..200: a = 2 * measure $0;
 IDENTIFIER@181..182: a
+BIN_EXPR@185..199: 2 * measure $0
 LITERAL@185..186: 2
 MEASURE_EXPRESSION@189..199: measure $0
 HARDWARE_QUBIT@197..199: $0
-EXPR_STMT@201..233: a = (measure $0) + (measure $1);
-BIN_EXPR@201..232: a = (measure $0) + (measure $1)
-ASSIGNMENT_STMT@201..217: a = (measure $0)
+ASSIGNMENT_STMT@201..233: a = (measure $0) + (measure $1);
 IDENTIFIER@201..202: a
+BIN_EXPR@205..232: (measure $0) + (measure $1)
 PAREN_EXPR@205..217: (measure $0)
 MEASURE_EXPRESSION@206..216: measure $0
 HARDWARE_QUBIT@214..216: $0
diff --git a/crates/pipeline-tests/tests/snapshots/runner__tests__snippets__reference__assignment__assignment.qasm-parse.snap b/crates/pipeline-tests/tests/snapshots/runner__tests__snippets__reference__assignment__assignment.qasm-parse.snap
index 66ff10f..d9daec2 100644
--- a/crates/pipeline-tests/tests/snapshots/runner__tests__snippets__reference__assignment__assignment.qasm-parse.snap
+++ b/crates/pipeline-tests/tests/snapshots/runner__tests__snippets__reference__assignment__assignment.qasm-parse.snap
@@ -7,7 +7,7 @@ expect-parse: Todo
 --- parser ---
 ok: false
 panicked: false
-errors: 3
+errors: 2
 --- ast ---
 SOURCE_FILE@0..161: 
 bit[2] a;
@@ -103,9 +103,8 @@ IDENTIFIER@143..144: q
 INDEX_OPERATOR@144..147: [0]
 EXPRESSION_LIST@145..146: 0
 LITERAL@145..146: 0
-EXPR_STMT@149..160: b = a == 0;
-BIN_EXPR@149..159: b = a == 0
-ASSIGNMENT_STMT@149..154: b = a
+ASSIGNMENT_STMT@149..160: b = a == 0;
 IDENTIFIER@149..150: b
+BIN_EXPR@153..159: a == 0
 IDENTIFIER@153..154: a
 LITERAL@158..159: 0