diff --git a/stdlib/openssl/0/openssl.rbs b/stdlib/openssl/0/openssl.rbs
index ebfde3072..677923e75 100644
--- a/stdlib/openssl/0/openssl.rbs
+++ b/stdlib/openssl/0/openssl.rbs
@@ -9332,7 +9332,8 @@ module OpenSSL
       # Reads *length* bytes from the SSL connection.  If a pre-allocated *buffer* is
       # provided the data will be written into it.
       #
-      def sysread_nonblock: (*untyped) -> untyped
+      def sysread_nonblock: (Integer length, ?String buffer, ?exception: true) -> String
+                          | (Integer length, ?String buffer, exception: false) -> (String | :wait_readable | :wait_writable | nil)
 
       # <!--
       #   rdoc-file=ext/openssl/ossl_ssl.c
@@ -9341,7 +9342,8 @@ module OpenSSL
       # Writes *string* to the SSL connection in a non-blocking manner.  Raises an
       # SSLError if writing would block.
       #
-      def syswrite_nonblock: (*untyped) -> untyped
+      def syswrite_nonblock: (_ToS string, ?exception: true) -> Integer
+                           | (_ToS string, exception: false) -> (Integer | :wait_readable | :wait_writable | nil)
 
       # <!--
       #   rdoc-file=ext/openssl/lib/openssl/ssl.rb
diff --git a/stdlib/socket/0/basic_socket.rbs b/stdlib/socket/0/basic_socket.rbs
index a69132467..ad51744b7 100644
--- a/stdlib/socket/0/basic_socket.rbs
+++ b/stdlib/socket/0/basic_socket.rbs
@@ -330,7 +330,8 @@ class BasicSocket < IO
   # ### See
   # *   Socket#recvfrom
   #
-  def recv_nonblock: (Integer maxlen, ?Integer flags, ?String buf, ?exception: boolish) -> (String | :wait_readable)
+  def recv_nonblock: (Integer maxlen, ?Integer flags, ?String buf, ?exception: true) -> String
+                   | (Integer maxlen, ?Integer flags, ?String buf, exception: false) -> (String | :wait_readable)
 
   # <!--
   #   rdoc-file=ext/socket/lib/socket.rb
@@ -401,7 +402,8 @@ class BasicSocket < IO
   # recvmsg_nonblock should not raise an IO::WaitReadable exception, but return
   # the symbol <code>:wait_readable</code> instead.
   #
-  def recvmsg_nonblock: (?Integer dlen, ?Integer flags, ?Integer clen, ?exception: boolish, ?scm_rights: boolish) -> ([ String, Addrinfo, Integer?, Array[Socket::AncillaryData] ] | :wait_readable)
+  def recvmsg_nonblock: (?Integer dlen, ?Integer flags, ?Integer clen, ?exception: true, ?scm_rights: boolish) -> [ String, Addrinfo, Integer?, Array[Socket::AncillaryData] ]
+                      | (?Integer dlen, ?Integer flags, ?Integer clen, exception: false, ?scm_rights: boolish) -> ([ String, Addrinfo, Integer?, Array[Socket::AncillaryData] ] | :wait_readable)
 
   # <!--
   #   rdoc-file=ext/socket/basicsocket.c
@@ -489,7 +491,8 @@ class BasicSocket < IO
   # sendmsg_nonblock should not raise an IO::WaitWritable exception, but return
   # the symbol <code>:wait_writable</code> instead.
   #
-  def sendmsg_nonblock: (String mesg, ?Integer flags, ?Addrinfo | String dest_sockaddr, *Socket::AncillaryData controls, ?exception: boolish) -> (Integer | :wait_writable)
+  def sendmsg_nonblock: (String mesg, ?Integer flags, ?Addrinfo | String dest_sockaddr, *Socket::AncillaryData controls, ?exception: true) -> Integer
+                      | (String mesg, ?Integer flags, ?Addrinfo | String dest_sockaddr, *Socket::AncillaryData controls, exception: false) -> (Integer | :wait_writable)
 
   # <!--
   #   rdoc-file=ext/socket/basicsocket.c
diff --git a/stdlib/socket/0/socket.rbs b/stdlib/socket/0/socket.rbs
index 63cb987fa..46116dc46 100644
--- a/stdlib/socket/0/socket.rbs
+++ b/stdlib/socket/0/socket.rbs
@@ -851,7 +851,8 @@ class Socket < BasicSocket
   # ### See
   # *   Socket#accept
   #
-  def accept_nonblock: (?exception: boolish) -> ([ Socket, Addrinfo ] | :wait_readable)
+  def accept_nonblock: (?exception: true) -> [ Socket, Addrinfo ]
+                     | (exception: false) -> ([ Socket, Addrinfo ] | :wait_readable)
 
   # <!--
   #   rdoc-file=ext/socket/socket.c
@@ -1105,7 +1106,8 @@ class Socket < BasicSocket
   # ### See
   # *   Socket#connect
   #
-  def connect_nonblock: (untyped addr, ?exception: untyped) -> (Integer | :wait_writable)
+  def connect_nonblock: (untyped addr, ?exception: true) -> Integer
+                      | (untyped addr, exception: false) -> (Integer | :wait_writable)
 
   # <!--
   #   rdoc-file=ext/socket/lib/socket.rb
@@ -1363,7 +1365,8 @@ class Socket < BasicSocket
   # ### See
   # *   Socket#recvfrom
   #
-  def recvfrom_nonblock: (Integer maxlen, ?Integer flags, ?untyped outbuf, ?exception: boolish) -> ([ String, Addrinfo ] | :wait_readable)
+  def recvfrom_nonblock: (Integer maxlen, ?Integer flags, ?untyped outbuf, ?exception: true) -> [ String, Addrinfo ]
+                       | (Integer maxlen, ?Integer flags, ?untyped outbuf, exception: false) -> ([ String, Addrinfo ] | :wait_readable)
 
   # <!--
   #   rdoc-file=ext/socket/socket.c
diff --git a/stdlib/socket/0/tcp_server.rbs b/stdlib/socket/0/tcp_server.rbs
index 05f3d3f47..0d6fc8bed 100644
--- a/stdlib/socket/0/tcp_server.rbs
+++ b/stdlib/socket/0/tcp_server.rbs
@@ -78,7 +78,8 @@ class TCPServer < TCPSocket
   # *   TCPServer#accept
   # *   Socket#accept
   #
-  def accept_nonblock: (?exception: boolish) -> (TCPSocket | :wait_readable)
+  def accept_nonblock: (?exception: true) -> TCPSocket
+                     | (exception: false) -> (TCPSocket | :wait_readable)
 
   # <!--
   #   rdoc-file=ext/socket/tcpserver.c
diff --git a/stdlib/socket/0/udp_socket.rbs b/stdlib/socket/0/udp_socket.rbs
index 0def4587f..1ee3b3170 100644
--- a/stdlib/socket/0/udp_socket.rbs
+++ b/stdlib/socket/0/udp_socket.rbs
@@ -86,7 +86,8 @@ class UDPSocket < IPSocket
   # ### See
   # *   Socket#recvfrom
   #
-  def recvfrom_nonblock: (Integer len, ?Integer flag, ?String outbuf, ?exception: boolish) -> [ String, [ String, Integer, String, String ] ]
+  def recvfrom_nonblock: (Integer len, ?Integer flag, ?String outbuf, ?exception: true) -> [ String, [ String, Integer, String, String ] ]
+                       | (Integer len, ?Integer flag, ?String outbuf, exception: false) -> ([ String, [ String, Integer, String, String ] ] | :wait_readable)
 
   # <!--
   #   rdoc-file=ext/socket/udpsocket.c
diff --git a/stdlib/socket/0/unix_server.rbs b/stdlib/socket/0/unix_server.rbs
index a8565ddaa..0a83f323c 100644
--- a/stdlib/socket/0/unix_server.rbs
+++ b/stdlib/socket/0/unix_server.rbs
@@ -56,7 +56,8 @@ class UNIXServer < UNIXSocket
   # *   UNIXServer#accept
   # *   Socket#accept
   #
-  def accept_nonblock: (?exception: boolish) -> (UNIXSocket | :wait_readable)
+  def accept_nonblock: (?exception: true) -> UNIXSocket
+                     | (exception: false) -> (UNIXSocket | :wait_readable)
 
   # <!--
   #   rdoc-file=ext/socket/unixserver.c