diff --git a/src/tint/reader/wgsl/lexer.cc b/src/tint/reader/wgsl/lexer.cc
index 89804f2..6371db7 100644
--- a/src/tint/reader/wgsl/lexer.cc
+++ b/src/tint/reader/wgsl/lexer.cc
@@ -96,9 +96,10 @@
     while (true) {
         tokens.emplace_back(next());
 
-        // If the token can be split, we insert a placeholder element into
-        // the stream to hold the split character.
-        if (tokens.back().IsSplittable()) {
+        // If the token can be split, we insert a placeholder element(s) into the stream to hold the
+        // split character.
+        size_t num_placeholders = tokens.back().NumPlaceholders();
+        for (size_t i = 0; i < num_placeholders; i++) {
             auto src = tokens.back().source();
             src.range.begin.column++;
             tokens.emplace_back(Token(Token::Type::kPlaceholder, src));
diff --git a/src/tint/reader/wgsl/lexer_test.cc b/src/tint/reader/wgsl/lexer_test.cc
index ffa85bd..a1a4764 100644
--- a/src/tint/reader/wgsl/lexer_test.cc
+++ b/src/tint/reader/wgsl/lexer_test.cc
@@ -989,7 +989,6 @@
                                          TokenData{"&=", Token::Type::kAndEqual},
                                          TokenData{"|=", Token::Type::kOrEqual},
                                          TokenData{"^=", Token::Type::kXorEqual},
-                                         TokenData{">>=", Token::Type::kShiftRightEqual},
                                          TokenData{"<<=", Token::Type::kShiftLeftEqual}));
 
 using SplittablePunctuationTest = testing::TestWithParam<TokenData>;
@@ -1010,18 +1009,23 @@
         EXPECT_EQ(t.source().range.end.column, 1u + strlen(params.input));
     }
 
-    {
-        auto& t = list[1];
+    const size_t num_placeholders = list[0].NumPlaceholders();
+    EXPECT_GT(num_placeholders, 0u);
+    ASSERT_EQ(list.size(), 2u + num_placeholders);
+
+    for (size_t i = 0; i < num_placeholders; i++) {
+        auto& t = list[1 + i];
         EXPECT_TRUE(t.Is(Token::Type::kPlaceholder));
         EXPECT_EQ(t.source().range.begin.line, 1u);
-        EXPECT_EQ(t.source().range.begin.column, 2u);
+        EXPECT_EQ(t.source().range.begin.column, 2u + i);
         EXPECT_EQ(t.source().range.end.line, 1u);
         EXPECT_EQ(t.source().range.end.column, 1u + strlen(params.input));
     }
 
     {
-        auto& t = list[2];
-        EXPECT_EQ(t.source().range.begin.column, 1 + std::string(params.input).size());
+        auto& t = list.back();
+        EXPECT_TRUE(t.Is(Token::Type::kEOF));
+        EXPECT_EQ(t.source().range.begin.column, 2u + num_placeholders);
     }
 }
 INSTANTIATE_TEST_SUITE_P(LexerTest,
@@ -1029,7 +1033,8 @@
                          testing::Values(TokenData{"&&", Token::Type::kAndAnd},
                                          TokenData{">=", Token::Type::kGreaterThanEqual},
                                          TokenData{"--", Token::Type::kMinusMinus},
-                                         TokenData{">>", Token::Type::kShiftRight}));
+                                         TokenData{">>", Token::Type::kShiftRight},
+                                         TokenData{">>=", Token::Type::kShiftRightEqual}));
 
 using KeywordTest = testing::TestWithParam<TokenData>;
 TEST_P(KeywordTest, Parses) {
diff --git a/src/tint/reader/wgsl/token.h b/src/tint/reader/wgsl/token.h
index 2aeffa9..1c8531b 100644
--- a/src/tint/reader/wgsl/token.h
+++ b/src/tint/reader/wgsl/token.h
@@ -379,10 +379,20 @@
         return type_ == Type::kVec2 || type_ == Type::kVec3 || type_ == Type::kVec4;
     }
 
-    /// @returns true if the token can be split during parse into component tokens
-    bool IsSplittable() const {
-        return Is(Type::kShiftRight) || Is(Type::kGreaterThanEqual) || Is(Type::kAndAnd) ||
-               Is(Type::kMinusMinus);
+    /// @returns the number of placeholder tokens required to follow the token, in order to provide
+    /// space for token splitting.
+    size_t NumPlaceholders() const {
+        switch (type_) {
+            case Type::kShiftRightEqual:
+                return 2;
+            case Type::kShiftRight:
+            case Type::kGreaterThanEqual:
+            case Type::kAndAnd:
+            case Type::kMinusMinus:
+                return 1;
+            default:
+                return 0;
+        }
     }
 
     /// @returns true if the token is a binary operator