diff --git a/lib/jwt.rb b/lib/jwt.rb
index 47c8580b..5edc3824 100644
--- a/lib/jwt.rb
+++ b/lib/jwt.rb
@@ -1,6 +1,7 @@
 # frozen_string_literal: true
 
-require 'base64'
+require 'jwt/base64'
+require 'jwt/json'
 require 'jwt/decode'
 require 'jwt/default_options'
 require 'jwt/encode'
@@ -17,12 +18,13 @@ module JWT
   module_function
 
   def encode(payload, key, algorithm = 'HS256', header_fields = {})
-    encoder = Encode.new payload, key, algorithm, header_fields
-    encoder.segments
+    Encode.new(payload: payload,
+               key: key,
+               algorithm: algorithm,
+               headers: header_fields).segments
   end
 
   def decode(jwt, key = nil, verify = true, options = {}, &keyfinder)
-    decoder = Decode.new(jwt, key, verify, DEFAULT_OPTIONS.merge(options), &keyfinder)
-    decoder.decode_segments
+    Decode.new(jwt, key, verify, DEFAULT_OPTIONS.merge(options), &keyfinder).decode_segments
   end
 end
diff --git a/lib/jwt/base64.rb b/lib/jwt/base64.rb
new file mode 100644
index 00000000..e69808b1
--- /dev/null
+++ b/lib/jwt/base64.rb
@@ -0,0 +1,19 @@
+# frozen_string_literal: true
+
+require 'base64'
+
+module JWT
+  # Base64 helpers
+  class Base64
+    class << self
+      def url_encode(str)
+        ::Base64.encode64(str).tr('+/', '-_').gsub(/[\n=]/, '')
+      end
+
+      def url_decode(str)
+        str += '=' * (4 - str.length.modulo(4))
+        ::Base64.decode64(str.tr('-_', '+/'))
+      end
+    end
+  end
+end
diff --git a/lib/jwt/decode.rb b/lib/jwt/decode.rb
index c6a6f543..37ee2e0e 100644
--- a/lib/jwt/decode.rb
+++ b/lib/jwt/decode.rb
@@ -8,11 +8,6 @@
 module JWT
   # Decoding logic for JWT
   class Decode
-    def self.base64url_decode(str)
-      str += '=' * (4 - str.length.modulo(4))
-      Base64.decode64(str.tr('-_', '+/'))
-    end
-
     def initialize(jwt, key, verify, options, &keyfinder)
       raise(JWT::DecodeError, 'Nil JSON web token') unless jwt
       @jwt = jwt
@@ -80,7 +75,7 @@ def segment_length
     end
 
     def decode_crypto
-      @signature = Decode.base64url_decode(@segments[2])
+      @signature = JWT::Base64.url_decode(@segments[2])
     end
 
     def header
@@ -96,7 +91,7 @@ def signing_input
     end
 
     def parse_and_decode(segment)
-      JSON.parse(Decode.base64url_decode(segment))
+      JSON.parse(JWT::Base64.url_decode(segment))
     rescue JSON::ParserError
       raise JWT::DecodeError, 'Invalid segment encoding'
     end
diff --git a/lib/jwt/encode.rb b/lib/jwt/encode.rb
index 7e8f07d4..8769e7f4 100644
--- a/lib/jwt/encode.rb
+++ b/lib/jwt/encode.rb
@@ -1,51 +1,76 @@
 # frozen_string_literal: true
 
-require 'json'
-
 # JWT::Encode module
 module JWT
   # Encoding logic for JWT
   class Encode
-    attr_reader :payload, :key, :algorithm, :header_fields, :segments
+    ALG_NONE = 'none'.freeze
+    ALG_KEY  = 'alg'.freeze
+    EXP_KEY  = 'exp'.freeze
+    EXP_KEYS = [EXP_KEY, EXP_KEY.to_sym].freeze
 
-    def self.base64url_encode(str)
-      Base64.encode64(str).tr('+/', '-_').gsub(/[\n=]/, '')
+    def initialize(options)
+      @payload   = options[:payload]
+      @key       = options[:key]
+      @algorithm = options[:algorithm]
+      @headers   = options[:headers]
     end
 
-    def initialize(payload, key, algorithm, header_fields)
-      @payload = payload
-      @key = key
-      @algorithm = algorithm
-      @header_fields = header_fields
-      @segments = encode_segments
+    def segments
+      @segments ||= combine(encoded_header_and_payload, encoded_signature)
     end
 
     private
 
+    def validate_payload!
+      return unless @payload && @payload.is_a?(Hash)
+
+      validate_exp!
+    end
+
+    def validate_exp!
+      return if EXP_KEYS.all? { |key| !@payload.key?(key) || @payload[key].is_a?(Integer) }
+
+      raise InvalidPayload, 'exp claim must be an integer'
+    end
+
     def encoded_header
-      header = { 'alg' => @algorithm }.merge(@header_fields)
-      Encode.base64url_encode(JSON.generate(header))
+      @encoded_header ||= encode_header
     end
 
     def encoded_payload
-      raise InvalidPayload, 'exp claim must be an integer' if @payload && @payload.is_a?(Hash) && @payload.key?('exp') && !@payload['exp'].is_a?(Integer)
-      Encode.base64url_encode(JSON.generate(@payload))
+      @encoded_payload ||= encode_payload
+    end
+
+    def encoded_signature
+      @encoded_signature ||= encode_signature
+    end
+
+    def encoded_header_and_payload
+      @encoded_header_and_payload ||= combine(encoded_header, encoded_payload)
+    end
+
+    def encode_header
+      encode(@headers.merge(ALG_KEY => @algorithm))
+    end
+
+    def encode_payload
+      validate_payload!
+      encode(@payload)
+    end
+
+    def encode_signature
+      return '' if @algorithm == ALG_NONE
+
+      JWT::Base64.url_encode(JWT::Signature.sign(@algorithm, encoded_header_and_payload, @key))
     end
 
-    def encoded_signature(signing_input)
-      if @algorithm == 'none'
-        ''
-      else
-        signature = JWT::Signature.sign(@algorithm, signing_input, @key)
-        Encode.base64url_encode(signature)
-      end
+    def encode(data)
+      JWT::Base64.url_encode(JWT::JSON.generate(data))
     end
 
-    def encode_segments
-      header = encoded_header
-      payload = encoded_payload
-      signature = encoded_signature([header, payload].join('.'))
-      [header, payload, signature].join('.')
+    def combine(*parts)
+      parts.join('.')
     end
   end
 end
diff --git a/lib/jwt/json.rb b/lib/jwt/json.rb
new file mode 100644
index 00000000..dffda08f
--- /dev/null
+++ b/lib/jwt/json.rb
@@ -0,0 +1,18 @@
+# frozen_string_literal: true
+
+require 'json'
+
+module JWT
+  # JSON wrapper
+  class JSON
+    class << self
+      def generate(data)
+        ::JSON.generate(data)
+      end
+
+      def parse(data)
+        ::JSON.parse(data)
+      end
+    end
+  end
+end
diff --git a/lib/jwt/jwk/rsa.rb b/lib/jwt/jwk/rsa.rb
index e4fe552a..4691de75 100644
--- a/lib/jwt/jwk/rsa.rb
+++ b/lib/jwt/jwk/rsa.rb
@@ -27,16 +27,16 @@ def kid
       def export
         {
           kty: KTY,
-          n: Base64.urlsafe_encode64(public_key.n.to_s(BINARY), padding: false),
-          e: Base64.urlsafe_encode64(public_key.e.to_s(BINARY), padding: false),
+          n: ::Base64.urlsafe_encode64(public_key.n.to_s(BINARY), padding: false),
+          e: ::Base64.urlsafe_encode64(public_key.e.to_s(BINARY), padding: false),
           kid: kid
         }
       end
 
       def self.import(jwk_data)
         imported_key = OpenSSL::PKey::RSA.new
-        imported_key.set_key(OpenSSL::BN.new(Base64.urlsafe_decode64(jwk_data[:n]), BINARY),
-          OpenSSL::BN.new(Base64.urlsafe_decode64(jwk_data[:e]), BINARY),
+        imported_key.set_key(OpenSSL::BN.new(::Base64.urlsafe_decode64(jwk_data[:n]), BINARY),
+          OpenSSL::BN.new(::Base64.urlsafe_decode64(jwk_data[:e]), BINARY),
           nil)
         self.new(imported_key)
       end
diff --git a/spec/jwt_spec.rb b/spec/jwt_spec.rb
index 65085aff..cccd3c20 100644
--- a/spec/jwt_spec.rb
+++ b/spec/jwt_spec.rb
@@ -57,21 +57,33 @@
       expect(header['alg']).to eq alg
       expect(jwt_payload).to eq payload
     end
+  end
 
-    it 'should display a better error message if payload exp is_a?(Time)' do
-      payload['exp'] = Time.now
+  context 'payload validation' do
+    subject { JWT.encode(payload, nil, 'none') }
+    let(:payload) { { 'exp' => exp } }
 
-      expect do
-        JWT.encode payload, nil, alg
-      end.to raise_error JWT::InvalidPayload
+    context 'when exp is given as a non Integer' do
+      let(:exp) { Time.now.to_i.to_s }
+      it 'raises an JWT::InvalidPayload error' do
+        expect { subject }.to raise_error(JWT::InvalidPayload, 'exp claim must be an integer')
+      end
     end
 
-    it 'should display a better error message if payload exp is not an Integer' do
-      payload['exp'] = Time.now.to_i.to_s
+    context 'when exp is given as an Integer' do
+      let(:exp) { 1234 }
 
-      expect do
-        JWT.encode payload, nil, alg
-      end.to raise_error JWT::InvalidPayload
+      it 'encodes the payload' do
+        expect(subject).to be_a(String)
+      end
+    end
+
+    context 'when the key for exp is a symbol' do
+      let(:payload) { { :exp => 'NotAInteger' } }
+
+      it 'raises an JWT::InvalidPayload error' do
+        expect { subject }.to raise_error(JWT::InvalidPayload, 'exp claim must be an integer')
+      end
     end
   end
 
@@ -228,7 +240,7 @@
         translated_alg  = alg.gsub('PS', 'sha')
         valid_signature = data[:rsa_public].verify_pss(
           translated_alg,
-          JWT::Decode.base64url_decode(signature),
+          JWT::Base64.url_decode(signature),
           [header, body].join('.'),
           salt_length: :auto,
           mgf1_hash:   translated_alg
@@ -339,7 +351,7 @@
   context 'Base64' do
     it 'urlsafe replace + / with - _' do
       allow(Base64).to receive(:encode64) { 'string+with/non+url-safe/characters_' }
-      expect(JWT::Encode.base64url_encode('foo')).to eq('string-with_non-url-safe_characters_')
+      expect(JWT::Base64.url_encode('foo')).to eq('string-with_non-url-safe_characters_')
     end
   end
 
@@ -364,4 +376,12 @@
       JWT.encode 'Hello World', 'secret'
     end.not_to raise_error
   end
+
+  context 'when the alg value is given as a header parameter' do
+
+    it 'does not override the actual algorithm used' do
+      headers = JSON.parse(::JWT::Base64.url_decode(JWT.encode('Hello World', 'secret', 'HS256', { alg: 'HS123'}).split('.').first))
+      expect(headers['alg']).to eq('HS256')
+    end
+  end
 end