diff --git a/test/openssl/test_asn1.rb b/test/openssl/test_asn1.rb
index 3e7f8c13ce..1170703775 100644
--- a/test/openssl/test_asn1.rb
+++ b/test/openssl/test_asn1.rb
@@ -379,11 +379,16 @@ class  OpenSSL::TestASN1 < OpenSSL::TestCase
   def test_utctime
     encode_decode_test B(%w{ 17 0D }) + "160908234339Z".b,
       OpenSSL::ASN1::UTCTime.new(Time.utc(2016, 9, 8, 23, 43, 39))
-    # possible range of UTCTime is 1969-2068 currently
-    encode_decode_test B(%w{ 17 0D }) + "690908234339Z".b,
-      OpenSSL::ASN1::UTCTime.new(Time.utc(1969, 9, 8, 23, 43, 39))
-    decode_test B(%w{ 17 0B }) + "6909082343Z".b,
-      OpenSSL::ASN1::UTCTime.new(Time.utc(1969, 9, 8, 23, 43, 0))
+    # Seconds is omitted
+    decode_test B(%w{ 17 0B }) + "1609082343Z".b,
+      OpenSSL::ASN1::UTCTime.new(Time.utc(2016, 9, 8, 23, 43, 0))
+    begin
+      # possible range of UTCTime is 1969-2068 currently
+      encode_decode_test B(%w{ 17 0D }) + "690908234339Z".b,
+        OpenSSL::ASN1::UTCTime.new(Time.utc(1969, 9, 8, 23, 43, 39))
+    rescue OpenSSL::ASN1::ASN1Error
+      pend "No negative time_t support?"
+    end
     # not implemented
     # decode_test B(%w{ 17 11 }) + "500908234339+0930".b,
     #   OpenSSL::ASN1::UTCTime.new(Time.new(1950, 9, 8, 23, 43, 39, "+09:30"))
diff --git a/test/openssl/test_fips.rb b/test/openssl/test_fips.rb
index a4ab87f384..a577d7891e 100644
--- a/test/openssl/test_fips.rb
+++ b/test/openssl/test_fips.rb
@@ -10,13 +10,20 @@ class OpenSSL::TestFIPS < OpenSSL::TestCase
   end
 
   def test_fips_mode_get
-    if OpenSSL::OPENSSL_FIPS
-      OpenSSL.fips_mode = true
-      assert OpenSSL.fips_mode == true, ".fips_mode returns true when .fips_mode=true"
+    return unless OpenSSL::OPENSSL_FIPS
+    assert_separately([{ "OSSL_MDEBUG" => nil }, "-ropenssl"], <<~"end;")
+      require #{__FILE__.dump}
 
-      OpenSSL.fips_mode = false
-      assert OpenSSL.fips_mode == false, ".fips_mode returns false when .fips_mode=false"
-    end
+      begin
+        OpenSSL.fips_mode = true
+        assert OpenSSL.fips_mode == true, ".fips_mode returns true when .fips_mode=true"
+
+        OpenSSL.fips_mode = false
+        assert OpenSSL.fips_mode == false, ".fips_mode returns false when .fips_mode=false"
+      rescue OpenSSL::OpenSSLError
+        pend "Could not set FIPS mode (OpenSSL::OpenSSLError: \#$!); skipping"
+      end
+    end;
   end
 end
 
diff --git a/test/openssl/test_pair.rb b/test/openssl/test_pair.rb
index 89cf41a86b..f22183446f 100644
--- a/test/openssl/test_pair.rb
+++ b/test/openssl/test_pair.rb
@@ -238,44 +238,42 @@ module OpenSSL::TestPairM
     }
   end
 
-  def write_nonblock(socket, meth, str)
-    ret = socket.send(meth, str)
-    ret.is_a?(Symbol) ? 0 : ret
-  end
-
-  def write_nonblock_no_ex(socket, str)
-    ret = socket.write_nonblock str, exception: false
-    ret.is_a?(Symbol) ? 0 : ret
-  end
-
   def test_write_nonblock
     ssl_pair {|s1, s2|
-      n = 0
-      begin
-        n += write_nonblock s1, :write_nonblock, "a" * 100000
-        n += write_nonblock s1, :write_nonblock, "b" * 100000
-        n += write_nonblock s1, :write_nonblock, "c" * 100000
-        n += write_nonblock s1, :write_nonblock, "d" * 100000
-        n += write_nonblock s1, :write_nonblock, "e" * 100000
-        n += write_nonblock s1, :write_nonblock, "f" * 100000
-      rescue IO::WaitWritable
+      assert_equal 3, s1.write_nonblock("foo")
+      assert_equal "foo", s2.read(3)
+
+      data = "x" * 16384
+      written = 0
+      while true
+        begin
+          written += s1.write_nonblock(data)
+        rescue IO::WaitWritable, IO::WaitReadable
+          break
+        end
       end
-      s1.close
-      assert_equal(n, s2.read.length)
+      assert written > 0
+      assert_equal written, s2.read(written).bytesize
     }
   end
 
   def test_write_nonblock_no_exceptions
     ssl_pair {|s1, s2|
-      n = 0
-      n += write_nonblock_no_ex s1, "a" * 100000
-      n += write_nonblock_no_ex s1, "b" * 100000
-      n += write_nonblock_no_ex s1, "c" * 100000
-      n += write_nonblock_no_ex s1, "d" * 100000
-      n += write_nonblock_no_ex s1, "e" * 100000
-      n += write_nonblock_no_ex s1, "f" * 100000
-      s1.close
-      assert_equal(n, s2.read.length)
+      assert_equal 3, s1.write_nonblock("foo", exception: false)
+      assert_equal "foo", s2.read(3)
+
+      data = "x" * 16384
+      written = 0
+      while true
+        case ret = s1.write_nonblock(data, exception: false)
+        when :wait_readable, :wait_writable
+          break
+        else
+          written += ret
+        end
+      end
+      assert written > 0
+      assert_equal written, s2.read(written).bytesize
     }
   end