diff --git a/fuzz/fuzz_seeds/postgres_2829_unary_minus_caret.sql b/fuzz/fuzz_seeds/postgres_2829_unary_minus_caret.sql
new file mode 100644
index 0000000000..1d1b4ffa2f
--- /dev/null
+++ b/fuzz/fuzz_seeds/postgres_2829_unary_minus_caret.sql
@@ -0,0 +1 @@
+SELECT -1 ^ 0;
diff --git a/src/dialect/mod.rs b/src/dialect/mod.rs
index 22e3fa367a..03cd295d4b 100644
--- a/src/dialect/mod.rs
+++ b/src/dialect/mod.rs
@@ -1152,7 +1152,7 @@ pub trait Dialect: Debug + Any {
             Precedence::Period => 100,
             Precedence::DoubleColon => 50,
             Precedence::AtTz => 41,
-            Precedence::MulDivModOp => 40,
+            Precedence::MulDivModOp | Precedence::UnaryPlusMinus => 40,
             Precedence::PlusMinus => 30,
             Precedence::Xor => 24,
             Precedence::Ampersand => 23,
@@ -2362,6 +2362,8 @@ pub enum Precedence {
     DoubleColon,
     /// Timezone operator (e.g. `AT TIME ZONE`).
     AtTz,
+    /// Unary `+` and `-`, bounding their operand.
+    UnaryPlusMinus,
     /// Multiplication / Division / Modulo operators (`*`, `/`, `%`).
     MulDivModOp,
     /// Addition / Subtraction (`+`, `-`).
diff --git a/src/dialect/postgresql.rs b/src/dialect/postgresql.rs
index 361396b5fe..ab63992032 100644
--- a/src/dialect/postgresql.rs
+++ b/src/dialect/postgresql.rs
@@ -208,6 +208,7 @@ pub struct PostgreSqlDialect {}
 const PERIOD_PREC: u8 = 200;
 const DOUBLE_COLON_PREC: u8 = 140;
 const BRACKET_PREC: u8 = 130;
+const UNARY_PLUS_MINUS_PREC: u8 = 125;
 const COLLATE_PREC: u8 = 120;
 const AT_TZ_PREC: u8 = 110;
 const CARET_PREC: u8 = 100;
@@ -387,6 +388,7 @@ impl Dialect for PostgreSqlDialect {
             Precedence::UnaryNot => NOT_PREC,
             Precedence::And => AND_PREC,
             Precedence::Or => OR_PREC,
+            Precedence::UnaryPlusMinus => UNARY_PLUS_MINUS_PREC,
         }
     }
 
diff --git a/src/dialect/sqlite.rs b/src/dialect/sqlite.rs
index 0124f1f645..3fbb35ebb2 100644
--- a/src/dialect/sqlite.rs
+++ b/src/dialect/sqlite.rs
@@ -128,7 +128,7 @@ impl Dialect for SQLiteDialect {
             Precedence::Period => 100,
             Precedence::DoubleColon => 50,
             Precedence::AtTz => 41,
-            Precedence::MulDivModOp => 40,
+            Precedence::MulDivModOp | Precedence::UnaryPlusMinus => 40,
             Precedence::PlusMinus => 30,
             Precedence::Xor => 25,
             Precedence::Ampersand => 24,
diff --git a/src/parser/mod.rs b/src/parser/mod.rs
index 1d6cc53417..b0f8f06461 100644
--- a/src/parser/mod.rs
+++ b/src/parser/mod.rs
@@ -2011,7 +2011,7 @@ impl<'a> Parser<'a> {
                 Ok(Expr::UnaryOp {
                     op,
                     expr: Box::new(
-                        self.parse_subexpr(self.dialect.prec_value(Precedence::MulDivModOp))?,
+                        self.parse_subexpr(self.dialect.prec_value(Precedence::UnaryPlusMinus))?,
                     ),
                 })
             }
diff --git a/tests/sqlparser_postgres.rs b/tests/sqlparser_postgres.rs
index 9fe435e7d5..c51fa86d23 100644
--- a/tests/sqlparser_postgres.rs
+++ b/tests/sqlparser_postgres.rs
@@ -13200,6 +13200,51 @@ fn parse_alter_table_no_inherit() {
     }
 }
 
+#[test]
+fn parse_pg_prefix_operator_before_multiplication() {
+    for sql in ["SELECT ~ 1 * 2", "SELECT |/ 25 * 4", "SELECT # 1 * 2"] {
+        let select = pg().verified_only_select(sql);
+        let Expr::UnaryOp { expr, .. } = expr_from_projection(&select.projection[0]) else {
+            panic!("Expected prefix operator expression in {sql}")
+        };
+        assert!(
+            matches!(
+                expr.as_ref(),
+                Expr::BinaryOp {
+                    op: BinaryOperator::Multiply,
+                    ..
+                }
+            ),
+            "{sql}"
+        );
+    }
+}
+
+#[test]
+fn parse_unary_plus_minus_before_pg_exponentiation() {
+    for (sql, unary_op, operand, exponent) in [
+        ("SELECT -1 ^ 0", UnaryOperator::Minus, "1", "0"),
+        ("SELECT +2 ^ 2", UnaryOperator::Plus, "2", "2"),
+    ] {
+        let select = pg().verified_only_select(sql);
+        let Expr::BinaryOp { left, op, right } = expr_from_projection(&select.projection[0]) else {
+            panic!("Expected exponentiation expression")
+        };
+        assert_eq!(*op, BinaryOperator::PGExp);
+        assert_eq!(
+            right.as_ref(),
+            &Expr::Value(number(exponent).with_empty_span())
+        );
+        assert_eq!(
+            left.as_ref(),
+            &Expr::UnaryOp {
+                op: unary_op,
+                expr: Box::new(Expr::Value(number(operand).with_empty_span())),
+            }
+        );
+    }
+}
+
 #[test]
 fn parse_create_function_cost() {
     let stmt = pg_and_generic()
@@ -13349,6 +13394,44 @@ fn parse_create_function_rows() {
     }
 }
 
+#[test]
+fn parse_unary_minus_before_pg_at_time_zone() {
+    let select = pg().verified_only_select("SELECT -ts AT TIME ZONE 'UTC'");
+    let Expr::AtTimeZone { timestamp, .. } = expr_from_projection(&select.projection[0]) else {
+        panic!("Expected AT TIME ZONE expression")
+    };
+    assert_eq!(
+        timestamp.as_ref(),
+        &Expr::UnaryOp {
+            op: UnaryOperator::Minus,
+            expr: Box::new(Expr::Identifier(Ident::new("ts"))),
+        }
+    );
+}
+
+#[test]
+fn parse_generic_unary_minus_before_caret() {
+    let statements = Parser::parse_sql(&GenericDialect {}, "SELECT -1 ^ 0").unwrap();
+    let Statement::Query(query) = &statements[0] else {
+        panic!("Expected query")
+    };
+    let SetExpr::Select(select) = query.body.as_ref() else {
+        panic!("Expected select")
+    };
+    let Expr::BinaryOp { left, op, right } = expr_from_projection(&select.projection[0]) else {
+        panic!("Expected bitwise expression")
+    };
+    assert_eq!(*op, BinaryOperator::BitwiseXor);
+    assert_eq!(
+        left.as_ref(),
+        &Expr::UnaryOp {
+            op: UnaryOperator::Minus,
+            expr: Box::new(Expr::Value(number("1").with_empty_span())),
+        }
+    );
+    assert_eq!(right.as_ref(), &Expr::Value(number("0").with_empty_span()));
+}
+
 #[test]
 fn parse_create_function_support() {
     let stmt = pg_and_generic().verified_stmt(