diff --git a/lib/faraday/deprecate.rb b/lib/faraday/deprecate.rb
index 53a199563..1e59b1894 100644
--- a/lib/faraday/deprecate.rb
+++ b/lib/faraday/deprecate.rb
@@ -8,13 +8,17 @@ module Faraday
   # @see Faraday::Deprecate
   module DeprecatedClass
     def self.proxy_class(new_klass)
-      Class.new(new_klass).tap do |k|
-        class << k
+      Class.new(new_klass) do
+        class << self
           extend Faraday::Deprecate
           # Make this more human readable than #<Class:Faraday::ClientError>
-          klass_name = superclass.to_s[/^#<Class:(\w*::\w*)>$/, 1]
+          klass_name = superclass.to_s[/^#<Class:([\w:]+)>$/, 1]
           deprecate :new, "#{klass_name}.new", '1.0'
           deprecate :inherited, klass_name, '1.0'
+
+          def ===(other)
+            superclass === other || super
+          end
         end
       end
     end
diff --git a/spec/faraday/deprecate_spec.rb b/spec/faraday/deprecate_spec.rb
new file mode 100644
index 000000000..a4a25c748
--- /dev/null
+++ b/spec/faraday/deprecate_spec.rb
@@ -0,0 +1,69 @@
+# frozen_string_literal: true
+
+RSpec.describe Faraday::DeprecatedClass do
+  class SampleClass < StandardError
+    attr_accessor :foo
+
+    def initialize(foo = nil)
+      @foo = foo || :foo
+    end
+  end
+
+  SampleDeprecatedClass = Faraday::DeprecatedClass.proxy_class(SampleClass)
+
+  it 'does not raise error for deprecated classes but prints an error message' do
+    error_message, foobar = with_warn_squelching { SampleDeprecatedClass.new(:foo_bar) }
+    expect(foobar).to be_a(SampleClass)
+    expect(foobar.foo).to eq(:foo_bar)
+    expect(error_message).to match(
+      Regexp.new(
+        'NOTE: SampleDeprecatedClass.new is deprecated; '\
+        'use SampleClass.new instead. It will be removed in or after version 1.0'
+      )
+    )
+  end
+
+  it 'does not raise an error for inherited error-namespaced classes but prints an error message' do
+    error_message, = with_warn_squelching { Class.new(SampleDeprecatedClass) }
+
+    expect(error_message).to match(
+      Regexp.new(
+        'NOTE: Inheriting SampleDeprecatedClass is deprecated; '\
+        'use SampleClass instead. It will be removed in or after version 1.0'
+      )
+    )
+  end
+
+  it 'allows backward-compatible class to be subclassed' do
+    expect {
+      with_warn_squelching { Class.new(SampleDeprecatedClass) }
+    }.not_to raise_error
+  end
+
+  it 'allows rescuing of a current error with a deprecated error' do
+    expect { raise SampleClass, nil }.to raise_error(SampleDeprecatedClass)
+  end
+
+  it 'allows rescuing of a current error with a current error' do
+    expect { raise SampleClass, nil }.to raise_error(SampleClass)
+  end
+
+  it 'allows rescuing of a deprecated error with a deprecated error' do
+    expect { raise SampleDeprecatedClass, nil }.to raise_error(SampleDeprecatedClass)
+  end
+
+  it 'allows rescuing of a deprecated error with a current error' do
+    expect { raise SampleDeprecatedClass, nil }.to raise_error(SampleClass)
+  end
+
+
+  def with_warn_squelching
+    stderr_catcher = StringIO.new
+    original_stderr = $stderr
+    $stderr = stderr_catcher
+    result = yield if block_given?
+    [stderr_catcher.tap(&:rewind).string, result]
+  ensure
+    $stderr = original_stderr
+  end
+end
diff --git a/spec/faraday/error_spec.rb b/spec/faraday/error_spec.rb
index 9b3292ad6..f99ae0071 100644
--- a/spec/faraday/error_spec.rb
+++ b/spec/faraday/error_spec.rb
@@ -56,7 +56,7 @@
       end
 
       it 'does not raise an error for inherited error-namespaced classes but prints an error message' do
-        error_message, = with_warn_squelching { class E < Faraday::Error::ClientError; end }
+        error_message, = with_warn_squelching { Class.new(Faraday::Error::ClientError) }
 
         expect(error_message).to match(
           Regexp.new(
@@ -67,7 +67,25 @@
       end
 
       it 'allows backward-compatible class to be subclassed' do
-        expect { class CustomError < Faraday::Error::ClientError; end }.not_to raise_error
+        expect {
+          with_warn_squelching { Class.new(Faraday::Error::ClientError) }
+        }.not_to raise_error
+      end
+
+      it 'allows rescuing of a current error with a deprecated error' do
+        expect { raise Faraday::ClientError, nil }.to raise_error(Faraday::Error::ClientError)
+      end
+
+      it 'allows rescuing of a current error with a current error' do
+        expect { raise Faraday::ClientError, nil }.to raise_error(Faraday::ClientError)
+      end
+
+      it 'allows rescuing of a deprecated error with a deprecated error' do
+        expect { raise Faraday::Error::ClientError, nil }.to raise_error(Faraday::Error::ClientError)
+      end
+
+      it 'allows rescuing of a deprecated error with a current error' do
+        expect { raise Faraday::Error::ClientError, nil }.to raise_error(Faraday::ClientError)
       end
     end