diff --git a/README.md b/README.md
index 484fdd9..71c80be 100644
--- a/README.md
+++ b/README.md
@@ -3,7 +3,7 @@
 [![npm](https://img.shields.io/npm/v/hyparquet-writer)](https://www.npmjs.com/package/hyparquet-writer)
 [![workflow status](https://github.com/hyparam/hyparquet-writer/actions/workflows/ci.yml/badge.svg)](https://github.com/hyparam/hyparquet-writer/actions)
 [![mit license](https://img.shields.io/badge/License-MIT-orange.svg)](https://opensource.org/licenses/MIT)
-![coverage](https://img.shields.io/badge/Coverage-96-darkred)
+![coverage](https://img.shields.io/badge/Coverage-95-darkred)
 [![dependencies](https://img.shields.io/badge/Dependencies-0-blueviolet)](https://www.npmjs.com/package/hyparquet?activeTab=dependencies)
 
 ## Usage
diff --git a/src/column.js b/src/column.js
index b579f51..2ee59fd 100644
--- a/src/column.js
+++ b/src/column.js
@@ -2,9 +2,9 @@ import { Encoding, PageType } from 'hyparquet/src/constants.js'
 import { unconvert } from './convert.js'
 import { writeRleBitPackedHybrid } from './encoding.js'
 import { writePlain } from './plain.js'
+import { getMaxDefinitionLevel, getMaxRepetitionLevel } from './schema.js'
 import { serializeTCompactProtocol } from './thrift.js'
 import { Writer } from './writer.js'
-import { getMaxDefinitionLevel, getMaxRepetitionLevel } from './schema.js'
 
 /**
  * @import {ColumnMetaData, DecodedArray, PageHeader, ParquetType, SchemaElement} from 'hyparquet'
@@ -18,22 +18,17 @@ export function writeColumn(writer, schemaPath, values) {
   const { type } = schemaElement
   if (!type) throw new Error(`column ${schemaElement.name} cannot determine type`)
   const offsetStart = writer.offset
+  const num_values = values.length
   let num_nulls = 0
 
-  // Unconvert type if necessary
-  values = unconvert(schemaElement, values)
-
-  // Write page to temp buffer
-  const page = new Writer()
-
-  /** @type {import('hyparquet/src/types.js').Encoding} */
-  const encoding = 'PLAIN'
+  // Write levels to temp buffer
+  const levels = new Writer()
 
   // TODO: repetition levels
   const maxRepetitionLevel = getMaxRepetitionLevel(schemaPath)
   let repetition_levels_byte_length = 0
   if (maxRepetitionLevel) {
-    repetition_levels_byte_length = writeRleBitPackedHybrid(page, [])
+    repetition_levels_byte_length = writeRleBitPackedHybrid(levels, [])
   }
 
   // definition levels
@@ -49,10 +44,15 @@ export function writeColumn(writer, schemaPath, values) {
         definitionLevels.push(maxDefinitionLevel)
       }
     }
-    definition_levels_byte_length = writeRleBitPackedHybrid(page, definitionLevels)
+    definition_levels_byte_length = writeRleBitPackedHybrid(levels, definitionLevels)
   }
 
-  // write page data
+  // Unconvert type and filter out nulls
+  values = unconvert(schemaElement, values)
+    .filter(v => v !== null && v !== undefined)
+
+  // write page data to temp buffer
+  const page = new Writer()
   writePageData(page, values, type)
 
   // TODO: compress page data
@@ -61,13 +61,13 @@ export function writeColumn(writer, schemaPath, values) {
   /** @type {PageHeader} */
   const header = {
     type: 'DATA_PAGE_V2',
-    uncompressed_page_size: page.offset,
-    compressed_page_size: page.offset,
+    uncompressed_page_size: levels.offset + page.offset,
+    compressed_page_size: levels.offset + page.offset,
     data_page_header_v2: {
-      num_values: values.length,
+      num_values,
       num_nulls,
-      num_rows: values.length,
-      encoding,
+      num_rows: num_values,
+      encoding: 'PLAIN',
       definition_levels_byte_length,
       repetition_levels_byte_length,
       is_compressed: false,
@@ -75,6 +75,9 @@ export function writeColumn(writer, schemaPath, values) {
   }
   writePageHeader(writer, header)
 
+  // write levels
+  writer.appendBuffer(levels.getBuffer())
+
   // write page data
   writer.appendBuffer(page.getBuffer())
 
@@ -83,7 +86,7 @@ export function writeColumn(writer, schemaPath, values) {
     encodings: ['PLAIN'],
     path_in_schema: schemaPath.slice(1).map(s => s.name),
     codec: 'UNCOMPRESSED',
-    num_values: BigInt(values.length),
+    num_values: BigInt(num_values),
     total_compressed_size: BigInt(writer.offset - offsetStart),
     total_uncompressed_size: BigInt(writer.offset - offsetStart),
     data_page_offset: BigInt(offsetStart),
diff --git a/src/encoding.js b/src/encoding.js
index ad20a94..fa30f0e 100644
--- a/src/encoding.js
+++ b/src/encoding.js
@@ -101,7 +101,8 @@ function writeRle(writer, values, bitWidth) {
       count++ // continue the run
     } else {
       // write the count of repeated values
-      writer.appendVarInt(count)
+      const header = count << 1
+      writer.appendVarInt(header)
 
       // write the value
       const width = bitWidth + 7 >> 3 // bytes needed
diff --git a/test/encoding.test.js b/test/encoding.test.js
index ad508d1..71b728f 100644
--- a/test/encoding.test.js
+++ b/test/encoding.test.js
@@ -56,4 +56,14 @@ describe('RLE bit-packed hybrid', () => {
     const decoded = roundTripDeserialize(original)
     expect(decoded).toEqual(original)
   })
+
+  it('should round-trip a sparse array of booleans', () => {
+    const original = Array(10000).fill(0)
+    original[10] = 1
+    original[100] = 1
+    original[500] = 1
+    original[9999] = 1
+    const decoded = roundTripDeserialize(original)
+    expect(decoded).toEqual(original)
+  })
 })
diff --git a/test/write.test.js b/test/write.test.js
index c973b61..db180c7 100644
--- a/test/write.test.js
+++ b/test/write.test.js
@@ -41,16 +41,30 @@ describe('parquetWrite', () => {
     ])
   })
 
-  it('efficiently serializes sparse booleans', () => {
+  it('efficiently serializes sparse booleans', async () => {
     const bool = Array(10000).fill(null)
     bool[10] = true
     bool[100] = false
     bool[500] = true
     bool[9999] = false
-    const buffer = parquetWrite([{ name: 'bool', data: bool }])
-    expect(buffer.byteLength).toBe(1399)
-    const metadata = parquetMetadata(buffer)
-    expect(metadata.metadata_length).toBe(89)
+    const file = parquetWrite([{ name: 'bool', data: bool }])
+    expect(file.byteLength).toBe(147)
+    const metadata = parquetMetadata(file)
+    expect(metadata.metadata_length).toBe(86)
+    const result = await parquetReadObjects({ file })
+    expect(result.length).toBe(10000)
+    expect(result[0]).toEqual({ bool: null })
+    expect(result[9]).toEqual({ bool: null })
+    expect(result[10]).toEqual({ bool: true })
+    expect(result[100]).toEqual({ bool: false })
+    expect(result[500]).toEqual({ bool: true })
+    expect(result[9999]).toEqual({ bool: false })
+  })
+
+  it('efficiently serializes long string', () => {
+    const str = 'a'.repeat(10000)
+    const file = parquetWrite([{ name: 'string', data: [str] }])
+    expect(file.byteLength).toBe(10136)
   })
 
   it('serializes list types', async () => {