diff --git a/cpp/src/parquet/column/levels-test.cc b/cpp/src/parquet/column/levels-test.cc
index b15c0af9bf482..cb7cc3863cdf6 100644
--- a/cpp/src/parquet/column/levels-test.cc
+++ b/cpp/src/parquet/column/levels-test.cc
@@ -183,4 +183,27 @@ TEST(TestLevels, TestLevelsDecodeMultipleSetData) {
   }
 }
 
+TEST(TestLevelEncoder, MinimumBufferSize) {
+  // PARQUET-676, PARQUET-698
+  const int kNumToEncode = 1024;
+
+  std::vector<int16_t> levels;
+  for (int i = 0; i < kNumToEncode; ++i) {
+    if (i % 9 == 0) {
+      levels.push_back(0);
+    } else {
+      levels.push_back(1);
+    }
+  }
+
+  std::vector<uint8_t> output(
+      LevelEncoder::MaxBufferSize(Encoding::RLE, 1, kNumToEncode));
+
+  LevelEncoder encoder;
+  encoder.Init(Encoding::RLE, 1, kNumToEncode, output.data(), output.size());
+  int encode_count = encoder.Encode(kNumToEncode, levels.data());
+
+  ASSERT_EQ(kNumToEncode, encode_count);
+}
+
 }  // namespace parquet
diff --git a/cpp/src/parquet/file/reader.cc b/cpp/src/parquet/file/reader.cc
index b6de168c2583e..50db1c0f2f105 100644
--- a/cpp/src/parquet/file/reader.cc
+++ b/cpp/src/parquet/file/reader.cc
@@ -162,8 +162,7 @@ void ParquetFileReader::DebugPrint(
       const ColumnStatistics stats = column_chunk->statistics();
 
       const ColumnDescriptor* descr = file_metadata->schema_descriptor()->Column(i);
-      stream << "Column " << i << std::endl
-             << ", values: " << column_chunk->num_values();
+      stream << "Column " << i << std::endl << ", values: " << column_chunk->num_values();
       if (column_chunk->is_stats_set()) {
         stream << ", null values: " << stats.null_count
                << ", distinct values: " << stats.distinct_count << std::endl
@@ -174,17 +173,15 @@ void ParquetFileReader::DebugPrint(
         stream << "  Statistics Not Set";
       }
       stream << std::endl
-             << "  compression: "
-             << compression_to_string(column_chunk->compression())
+             << "  compression: " << compression_to_string(column_chunk->compression())
              << ", encodings: ";
       for (auto encoding : column_chunk->encodings()) {
         stream << encoding_to_string(encoding) << " ";
       }
       stream << std::endl
-             << "  uncompressed size: "
-             << column_chunk->total_uncompressed_size()
-             << ", compressed size: "
-             << column_chunk->total_compressed_size() << std::endl;
+             << "  uncompressed size: " << column_chunk->total_uncompressed_size()
+             << ", compressed size: " << column_chunk->total_compressed_size()
+             << std::endl;
     }
 
     if (!print_values) { continue; }
diff --git a/cpp/src/parquet/util/rle-encoding.h b/cpp/src/parquet/util/rle-encoding.h
index b0fb8d1395e68..15fd5504ba17f 100644
--- a/cpp/src/parquet/util/rle-encoding.h
+++ b/cpp/src/parquet/util/rle-encoding.h
@@ -174,7 +174,14 @@ class RleEncoder {
     int bytes_per_run = BitUtil::Ceil(bit_width * MAX_VALUES_PER_LITERAL_RUN, 8.0);
     int num_runs = BitUtil::Ceil(num_values, MAX_VALUES_PER_LITERAL_RUN);
     int literal_max_size = num_runs + num_runs * bytes_per_run;
-    return std::max(MinBufferSize(bit_width), literal_max_size);
+
+    // In the very worst case scenario, the data is a concatenation of repeated
+    // runs of 8 values. Repeated run has a 1 byte varint followed by the
+    // bit-packed repeated value
+    int min_repeated_run_size = 1 + BitUtil::Ceil(bit_width, 8);
+    int repeated_max_size = BitUtil::Ceil(num_values, 8) * min_repeated_run_size;
+
+    return std::max(literal_max_size, repeated_max_size);
   }
 
   /// Encode value.  Returns true if the value fits in buffer, false otherwise.