diff --git a/Sources/OpenAPIRuntime/Conversion/Converter+Server.swift b/Sources/OpenAPIRuntime/Conversion/Converter+Server.swift
index 75b0f52..185711b 100644
--- a/Sources/OpenAPIRuntime/Conversion/Converter+Server.swift
+++ b/Sources/OpenAPIRuntime/Conversion/Converter+Server.swift
@@ -56,11 +56,42 @@ extension Converter {
                 // Drop everything after the optional semicolon (q, extensions, ...)
                 value.split(separator: ";")[0].trimmingCharacters(in: .whitespacesAndNewlines).lowercased()
             }
-
         if acceptValues.isEmpty { return }
-        if acceptValues.contains("*/*") { return }
-        if acceptValues.contains("\(substring.split(separator: "/")[0].lowercased())/*") { return }
-        if acceptValues.contains(where: { $0.localizedCaseInsensitiveContains(substring) }) { return }
+        guard let parsedSubstring = OpenAPIMIMEType(substring) else {
+            throw RuntimeError.invalidAcceptSubstring(substring)
+        }
+        // Look for the first match.
+        for acceptValue in acceptValues {
+            // Fast path.
+            if acceptValue == substring { return }
+            guard let parsedAcceptValue = OpenAPIMIMEType(acceptValue) else {
+                throw RuntimeError.invalidExpectedContentType(acceptValue)
+            }
+            switch (parsedAcceptValue.kind, parsedSubstring.kind) {
+            case (.any, _):
+                // Accept: */* always matches
+                return
+            case (.anySubtype(type: let acceptType), let substring):
+                switch substring {
+                case .any:
+                    // */* as a concrete content type is NOT a match for an Accept header of foo/*
+                    break
+                case .anySubtype(type: let substringType):
+                    // Only match if the types match.
+                    if substringType.lowercased() == acceptType.lowercased() { return }
+                case .concrete(type: let substringType, _):
+                    if substringType.lowercased() == acceptType.lowercased() { return }
+                }
+            case (.concrete(type: let acceptType, subtype: let acceptSubtype), let substring):
+                if case let .concrete(substringType, substringSubtype) = substring {
+                    if acceptType.lowercased() == substringType.lowercased()
+                        && acceptSubtype.lowercased() == substringSubtype.lowercased()
+                    {
+                        return
+                    }
+                }
+            }
+        }
         throw RuntimeError.unexpectedAcceptHeader(acceptHeader)
     }
 
diff --git a/Sources/OpenAPIRuntime/Errors/RuntimeError.swift b/Sources/OpenAPIRuntime/Errors/RuntimeError.swift
index b0c776e..549e3a1 100644
--- a/Sources/OpenAPIRuntime/Errors/RuntimeError.swift
+++ b/Sources/OpenAPIRuntime/Errors/RuntimeError.swift
@@ -21,6 +21,7 @@ internal enum RuntimeError: Error, CustomStringConvertible, LocalizedError, Pret
     case invalidServerURL(String)
     case invalidServerVariableValue(name: String, value: String, allowedValues: [String])
     case invalidExpectedContentType(String)
+    case invalidAcceptSubstring(String)
     case invalidHeaderFieldName(String)
     case invalidBase64String(String)
 
@@ -85,6 +86,7 @@ internal enum RuntimeError: Error, CustomStringConvertible, LocalizedError, Pret
             return
                 "Invalid server variable named: '\(name)', which has the value: '\(value)', but the only allowed values are: \(allowedValues.map { "'\($0)'" }.joined(separator: ", "))"
         case .invalidExpectedContentType(let string): return "Invalid expected content type: '\(string)'"
+        case .invalidAcceptSubstring(let string): return "Invalid Accept header content type: '\(string)'"
         case .invalidHeaderFieldName(let name): return "Invalid header field name: '\(name)'"
         case .invalidBase64String(let string):
             return "Invalid base64-encoded string (first 128 bytes): '\(string.prefix(128))'"
diff --git a/Tests/OpenAPIRuntimeTests/Conversion/Test_Converter+Server.swift b/Tests/OpenAPIRuntimeTests/Conversion/Test_Converter+Server.swift
index b2305a0..9e16fbf 100644
--- a/Tests/OpenAPIRuntimeTests/Conversion/Test_Converter+Server.swift
+++ b/Tests/OpenAPIRuntimeTests/Conversion/Test_Converter+Server.swift
@@ -39,18 +39,20 @@ final class Test_ServerConverterExtensions: Test_Runtime {
             .accept: "text/html, application/xhtml+xml, application/xml;q=0.9, image/webp, */*;q=0.8"
         ]
         let multiple: HTTPFields = [.accept: "text/plain, application/json"]
+        let params: HTTPFields = [.accept: "application/json; foo=bar"]
         let cases: [(HTTPFields, String, Bool)] = [
             // No Accept header, any string validates successfully
             (emptyHeaders, "foobar", true),
 
-            // Accept: */*, any string validates successfully
-            (wildcard, "foobar", true),
+            // Accept: */*, any MIME type validates successfully
+            (wildcard, "foobaz/bar", true),
 
             // Accept: text/*, so text/plain succeeds, application/json fails
             (partialWildcard, "text/plain", true), (partialWildcard, "application/json", false),
 
             // Accept: text/plain, text/plain succeeds, application/json fails
-            (short, "text/plain", true), (short, "application/json", false),
+            (short, "text/plain", true), (short, "application/json", false), (short, "application/*", false),
+            (short, "*/*", false),
 
             // A bunch of acceptable content types
             (long, "text/html", true), (long, "application/xhtml+xml", true), (long, "application/xml", true),
@@ -58,6 +60,10 @@ final class Test_ServerConverterExtensions: Test_Runtime {
 
             // Multiple values
             (multiple, "text/plain", true), (multiple, "application/json", true), (multiple, "application/xml", false),
+
+            // Params
+            (params, "application/json; foo=bar", true), (params, "application/json; charset=utf-8; foo=bar", true),
+            (params, "application/json", true), (params, "text/plain", false),
         ]
         for (headers, contentType, success) in cases {
             if success {